Riza and Roy are expecting, however creative differences leave them stuck on a name. All bets are on! Winry prided herself on her situational awareness, quick thinking, and high bullshit threshold.

According to some research, 20 percent of regular gamblers are problem or pathological gamblers. Moreover, when they gamble, they spend—which is to say, lose—more than other players. At least nine independent studies demonstrate that problem gamblers generate anywhere from 30 to 60 percent of total gambling revenues.

Casinos know exactly who their biggest spenders are. According to a article in Time magazine, back in the s casino operators bought records from credit-card companies and mailing lists from direct-mail marketers. These days, the casinos have their own internal methods for determining who their most attractive customers are.

Each time a patron hits the Spin or the Deal button, which can be as frequently as to 1, times an hour, the casino registers the data. In some machines, miniature cameras watch their faces and track their playing behavior. Several companies supply casinos with ATMs that allow patrons to withdraw funds through both debit and cash-advance functions, in some cases without ever leaving the machines they are playing.

Some of the companies also sell information on their ATM customers to the casinos. All of these data have enabled casinos to specifically target their most reliable spenders, primarily problem gamblers and outright addicts.

They also employ hosts who befriend large spenders and use special offers to encourage them to stay longer or return soon. Some hosts receive bonuses that are tied to the amount customers spend beyond their expected losses, which are calculated using the data gathered from previous visits.

The business plan for casinos is based on the addicted gambler. It increased the limits on some slot machines so that she could spend more on single games. It also made a new machine off-limits to other customers so that Richardson could be the first to play it. Management assigned Richardson an executive host, who offered her free drinks, meals, hotel stays, and tickets to entertainment events.

In , Richardson, then 54, was sentenced to 14 to 20 years in prison for the crime. The thefts ultimately put the company out of business. A representative for Ameristar Casino declined to comment on the lawsuit. The U. District Court for Nebraska agreed that Colombo had sufficiently proved its initial claim of unjust enrichment, which the casino would have to defend itself against.

W alk into the Mountaineer Casino in West Virginia, and the slot machines overwhelm you—more than 1, of them, lights blinking, animated screens flashing, the simulated sound of clinking coins blaring across the floor. But the vast majority sit at the slot machines.

Slots and video poker have become the lifeblood of the American casino. They generate nearly 70 percent of casino revenues, according to a American Gaming Association report, up from 45 percent four decades ago. Three out of five casino visitors say their favorite activity is playing electronic gaming machines. Their popularity spells profits not only for casinos but for manufacturers as well.

Old-fashioned three-reel slot machines consisted of physical reels that were set spinning by the pull of a lever. If the same symbol aligned on the payline on all three reels when they stopped spinning, the player would win a jackpot that varied in size depending on the symbol.

The odds were straightforward and not terribly hard to calculate. But where each reel stops is no longer determined by the force of a good pull of the lever. The physical reels are not spinning until they run out of momentum, as it might appear. Thus it is possible for game designers to reduce the odds of hitting a big jackpot from 1 in 10, to 1 in million. Moreover, it is almost impossible for a slots player to have any idea of the actual odds of winning any jackpot, however large or small.

The intent is to give the player the impression of having almost won—when, in fact, he or she is no closer to having won than if the symbol had not appeared on the reel at all. Some slot machines are specifically programmed to offer up this near-miss result far more often than they would if they operated by sheer chance, and the psychological impact can be powerful, leading players to think, I was so close.

Maybe next time. Nelson Rose, a professor at Whittier Law School and the author of Gambling and the Law , has written, Nevada regulations operate on the theory that a sophisticated player would be able to tell the real odds of winning by playing a machine long enough. Research has shown that an elevated number of near-miss results does increase playing time.

Indeed, as early as , B. In the United States, by contrast, the federal government granted the patent for virtual reel mapping in IGT purchased the rights to it in and later licensed the patent to other companies. Of course, classic, spinning-reel slot machines make up only a fraction of the electronic gaming machines available at most casinos.

Technology has evolved such that many machines lack physical reels altogether, instead merely projecting the likenesses of spinning symbols onto a video screen. Instead of betting on one simple payline, players are able to bet on multiple patterns of paylines—as many as on some machines.

This allows for more opportunities to win, but the results are often deceptive. You can get to of these false wins, which we also call losses , an hour. Because the machine is telling the player he or she is winning, the gradual siphoning is less noticeable. Related to the video slot machines are video-poker terminals, which IGT began popularizing in The standard five-card-draw game shows five cards, each offering players the option to hold or replace by drawing a card from the 47 remaining in the virtual deck.

The games require more skill—or at least a basic understanding of probabilities—than the slot machines do. As such, they appeal to people who want to have some sense of exerting control over the outcome. They saw, for instance, patrons going more often for four of a kind than the royal flush, a rarer but more lucrative hand, and they adjusted the machines accordingly. Video poker also offers its own version of losses disguised as wins. Whatever the exact figure, the house odds make it such that if a player plays long enough, she will eventually lose her money.

T echnological innovations have not only rendered electronic gaming machines wildly profitable; they have also, according to experts, made them more addictive. A crucial element in modern gambling machines is speed. Individual hands or spins can be completed in just three or four seconds.

For many gambling addicts, the zone itself becomes more desirable even than winning. Players have gone for 14, 15, 16 hours or more playing continuously. They have become so absorbed in the machines that they left their young children unattended in cars, wet themselves without noticing, and neglected to eat for hours.

Casinos and game designers have come up with many ways to keep patrons at their machines and playing rapidly. The chairs are ergonomically designed so that someone can sit comfortably for long stretches. Winnings can be converted back to credits or printed on vouchers to be redeemed later.

Waitresses come by to take drink orders, obviating the need for players to get up at all. Public-policy advocates compare slot machines to cigarettes. Both, they claim, are products specifically and deliberately engineered to have addictive properties that are known to hook users. Eubanks was the lead counsel for the Justice Department in successful federal litigation against the tobacco industry between and She joined Noffsinger in representing Stacy Stevens after he convinced her that the deception used by the gambling industry paralleled that of the tobacco industry.

The data they track in real time on player cards alert them to these pain points: a big loss, for instance, or when credits start to run low after a dry run. Hosts are also on the lookout for telling behavior, such as someone striking a machine in frustration or slumping over it in discouragement. When hosts spot someone in a state like this, they may swoop in and offer a voucher for some free credits, a drink, or perhaps a meal in the restaurant, where the player can take a break until the resistance passes and he can resume gambling.

When players do exhaust all their funds, casinos will sometimes loan them additional money. In , she spent an entire night gambling at Caesars Riverboat Casino, drinking strong alcoholic beverages provided for free. When she eventually came to the end of her money playing blackjack, the casino offered her a counter check, basically a promissory note, to enable her to keep playing.

She signed the check and gambled away the money. That happened five more times. Noffsinger countersued on her behalf. Experts say casinos should be aware that when they extend credit to losing patrons, they are by definition enabling problem gamblers.

Casinos might similarly be held liable for the financial consequences suffered by gamblers to whom they extend credit beyond a certain limit. In , the widow of a man who killed himself after racking up insurmountable debt at a Mississippi casino sued the casino under an extrapolation of dramshop laws.

So far, no U. Nor should they, according to the gambling industry. Nothing of that sort exists to measure what the level is to have gambled too much. Mountaineer Casino and IGT both declined repeated requests for comment. It does not, however, prevent them from losing money if they visit a casino despite the restriction. Some experts believe self-exclusion lists are not effective, because they seem to be erratically enforced. Despite the presence of sophisticated surveillance technology, patrons are not routinely screened for their self-exclusion status.

Given that casino operators and slot-machine manufacturers are adamant that the blame for gambling addiction resides with the individual, it is not surprising that research by the industry-funded National Center for Responsible Gaming favors studies directed toward confirming this conclusion.

Members of the board of directors, she asserts, do not make research decisions, and the center has a separate scientific advisory board. She says that the problem is rooted in the individual. Independent research not funded by the NCRG has shown how false wins, near misses, and other such features influence gamblers, especially the way they perceive expected outcomes.

Most of them are making correct conclusions based on deceptive information. Keith Whyte, the executive director of the National Council on Problem Gambling, says that although the industry should have a role in research and public-education efforts, it cannot be effective on its own.

The group, which maintains a neutral stance toward legal gambling, receives a large share of its funding from the industry. A lmost a decade after the Indian Gaming Regulatory Act launched the dramatic expansion of casino gambling into new jurisdictions, the federal government appointed a commission to study the impact of the proliferation.

Despite that warning, states have been unable to resist the continued expansion of casino gambling. One reason for the ongoing growth is the financial clout of the industry itself. Many states provide tribal casinos with regional monopolies in exchange for revenues skimmed off the top of casino profits—as much as 30 to 40 percent in some places.

Kansas actually owns the games and operations of nontribal casinos. New Jersey, Delaware, and Rhode Island have all provided financial bailouts to faltering casinos. Communities typically build casinos based on a mirage of false promises: that they will provide jobs, fund schools, and boost the local economy. It should not be allowed by anyone, anywhere, anytime.

In defense of its products and practices, the gambling industry insists that it is heavily regulated and therefore safe. Nelson Rose, the author of Gambling and the Law. Each state in which gambling is legal has set up its own commission to regulate the industry, but there seems to be a symbiotic relationship between regulators and the industry.

Many gaming-commission members—including those who approve applications for casino licenses—are advised by consultants for private companies also on casino payrolls. Yet such essential disclosure is not required of electronic gaming machines. Now imagine you want to find P A B , and the information shown on the branches above is all the information that you have. How can you use the probabilities you have to work out P A B?

To find P B , we use the same process that we used to find P Even earlier; we need to add together the probabilities of all the different ways in which the event we want can possibly happen. There are two ways in which even B can occur: either with event A, or without it. This means that we can find P B using:. We can rewrite this in terms of the probabilities we already know from the probability tree. This means that we can use:. This is sometimes known as the Law of Total Probability , as it gives a way of finding the total probability of a particular event based on conditional probabilities.

We started off by wanting to find P A B based on probabilities we already know from a probability tree. What we need is a general expression for finding conditional probabilities that are the reverse of what we already know, in other words P A B. And even though the formula is tricky, visualizing the problem can help. The Manic Mango games company is testing two brand-new games.

Manic Mango selects one of the volunteers at random to ask if she enjoyed playing the game, and she says she did. If you have two events A and B, then. If you have n mutually exclusive and exhaustive events, A 1 through to A n , and B is another event, then. It will give you the same result, and it can keep you from losing track of which probability belongs to which event.

Did we make a mistake? This means that P Even Green is 0; therefore, it has no effect on the calculation. Is that always the case? They are two separate probabilities, and making this sort of assumption could actually cost you valuable points in a statistics exam. For example, it can be used in computing as a way of filtering emails and detecting which ones are likely to be junk. Before you leave the roulette table, the croupier has offered you a great deal for your final bet, triple or nothing.

If you bet that the ball lands in a black pocket twice in a row, you could win back all of your chips. Notice that the probabilities for landing on two black pockets in a row are a bit different than they were in our probability tree in Bad luck! Take a look at the equation for this probability:. For P Even Black , the probability of getting an even pocket is affected by the event of getting a black. We already know that the ball has landed in a black pocket, so we use this knowledge to work out the probability.

We look at how many of the pockets are even out of all the black pockets. To work out P Even , we look at how many pockets are even out of all the pockets. P Even Black gives a different result from P Even. In other words, the knowledge we have that the pocket is black changes the probability.

These two events are said to be dependent. Look at the probability tree on the previous page again. What do you notice about the sets of branches? Are the events for getting a black in the first game and getting a black in the second game dependent? Not all events are dependent.

Sometimes events remain completely unaffected by each other, and the probability of an event occurring remains the same irrespective of whether the other event happens or not. What do you notice? These two probabilities have the same value.

In other words, the event of getting a black pocket in this game has no bearing on the probability of getting a black pocket in the next game. These events are independent. If one event occurs, the probability of the other occurring remains exactly the same. If events A and B are independent, then the probability of event A is unaffected by event B. In other words.

We can also use this as a test for independence. If A and B are mutually exclusive, then if event A occurs, event B cannot. In other words, if two events are independent, then you can work out the probability of getting both events A and B by multiplying their individual probabilities together.

As the events are independent, the result is. If A and B are mutually exclusive, then if event A happens, B cannot. Also, if event B happens, then A cannot. If A and B are independent, then the outcome of A has no effect on the outcome of B, and the outcome of B has no effect on the outcome of A. Their respective outcomes have no effect on each other. Q: Do both events have to be independent?

Can one event be independent and the other dependent? Q: Are all games on a roulette wheel independent? A: Yes, they are. Separate spins of the roulette wheel do not influence each other. In each game, the probabilities of the ball landing on a red, black, or green remain the same. How do I use a Venn diagram to tell if events are independent? Venn diagrams are great if you need to examine intersections and show mutually exclusive events.

The Case of the Two Classes. The Head First Health Club prides itself on its ability to find a class for everyone. As a result, it is extremely popular with both young and old. The Health Club is wondering how best to market its new yoga class, and the Head of Marketing wonders if someone who goes swimming is more likely to go to a yoga class. The CEO disagrees. They ask a group of 96 people whether they go to the swimming or yoga classes.

Out of these 96 people, 32 go to yoga and 72 go swimming. Are the yoga and swimming classes dependent or independent? Well, I hear you keep getting fledgling statisticians into trouble. You want to work out the probability of getting two independent events?

Just multiply the probabilities for the two events together and job done. With independent events, probabilities just turn out the same. I think that people need to think of me first instead of you; that would sort out all of these problems. By really thinking through whether events are dependent or not. Let me give you an example.

Suppose you have a deck of 52 cards, and thirteen of them are diamonds. What would be the probability of that happening? The events are dependent. You can no longer say there are 13 diamonds in a pack of 52 cards. Not fair, I assumed you put the first card back!

That would have meant the probability of getting a diamond would have been the same as before, and I would have been right. The events would have been independent. When people think about you first, it leads them towards making all sorts of inappropriate assumptions. Solved: The Case of the Two Classes. So how do we know the classes are independent? Here are a bunch of situations and events. Your task is to say which of these are dependent, and which are independent. Choosing a card from a deck of cards, putting the card back in the deck, and then choosing another one.

Your task was to say which of these are dependent, and which are independent. When you remove one sock, there are fewer socks to choose from the next time, and this affects the probability. Besides the chances of winning, you also need to know how much you stand to win in order to decide if the bet is worth the risk. Betting on an event that has a very low probability may be worth it if the payoff is high enough to compensate you for the risk. Fred decides to throw a coin. I person eats alone if Fred and George go to the Diner.

As these events are independent, this is equal to P 22 x P Skip to main content. Head First Statistics by Dawn Griffiths. Start your free trial. Calculating Probabilities: Taking Chances. Roll up for roulette! Your very own roulette board. Note Just be careful with those scissors.

Place your bets now! Brain Power What things do you need to think about before placing any roulette bets? What are the chances? Vital Statistics: Event An outcome or occurrence that has a probability assigned to it. Sharpen your pencil.

Sharpen your pencil Solution. Find roulette probabilities. You can visualize probabilities with a Venn diagram. Complementary events. BE the croupier Solution. Note The most likely event out of all these is that the ball will land in a black pocket.

There are no Dumb Questions. Q: Q: Why do I need to know about probability? Q: Q: Are probabilities written as fractions, decimals, or percentages? A: A: They can be written as any of these. A: A: There certainly is. Q: Q: Do I always have to draw a Venn diagram? A: A: No. And the winning number is You can also add probabilities. Vital Statistics: Probability To find the probability of an event A, use.

Q: Q: It looks like there are three ways of dealing with this sort of probability. A: A: It all depends on your particular situation and what information you are given. Q: Q: If some events are so unlikely to happen, why do people bet on them?

A: A: A lot depends on the sort of return that is being offered. Q: Q: Does adding probabilities together like that always work? A: A: Think of this as a special case where it does. You win! Time for another bet. Note Uh oh! Different answers. Exclusive events and intersecting events. Brain Power What sort of effect do you think this intersection could have had on the probability? Problems at the intersection. Some more notation. Watch it! BE the probability Solution. Exercise Solution.

A: A: Yes it is. Q: Q: Is there a limit on how many events can intersect? Another unlucky spin Conditions apply. Find conditional probabilities. Note The probability of A give that we know B has happened. You can visualize conditional probabilities with a probability tree. Trees also help you calculate conditional probabilities. Handy hints for working with trees. Probability Magnets Solution. You can get coffee with or without donuts. Note Hint: maybe some of your other answers can help you.

Note We can read this off the tree. Vital Statistics: Conditions. A: A: No, they refer to different probabilities. Q: Q: Are probability trees better than Venn diagrams? A: A: Both diagrams give you a way of visualizing probabilities, and both have their uses. Q: Q: Is there a limit to how many sets of branches you can have on a probability tree?

Bad luck! Note This is the opposite of the previous bet. We can find P Black l Even using the probabilities we already have. So where does this get us? Brain Power Take another look at the probability tree in So where does this get us?

Step 2: Finding P Even. Step 3: Finding P Black l Even. These results can be generalized to other problems. Brain Power Take a good look at the probability tree. How would you use it to find P B? Note Add together both of the intersections to get P B. Long Exercise Solution. Q: Q: Do I have to draw a probability tree?

We have a winner! If events affect each other, they are dependent. Note These two probabilities are different. Brain Power Look at the probability tree on the previous page again. If events do not affect each other, they are independent. Note These probabilities are the same. The events are independent. More on calculating probability for independent events. A: A: Imagine you have two events, A and B. Q: Q: Do both events have to be independent? Q: Q: Are all games on a roulette wheel independent?

A: A: Yes, they are. Five Minute Mystery. Dependent: Independent: Independent, glad you could show up. Really, Dependent? How come? Like how? What if you pick out a second card? Think nothing of it. Just make sure you think things through a bit more carefully next time. Five Minute Mystery Solved. Dependent or Independent?

It is in fact artificial to separate these factors since they all occur simultaneously for the compulsive gambler. Social meaning, psychological relief and a fired dopamine reward system can be a difficult combination of experiences for the most hardy of individuals to resist.

If you feel that you have lost control of your gambling, there are some things you can do to help yourself. Living with someone who gambles can be just as difficult as living with someone with any other kind of addiction. It can be very stressful and it can lead to the breakdown of your relationship. If you are not sure whether you are living with someone who has a gambling problem, ask yourself:.

Home A-to-z G Gambling and mental health Gambling and mental health People gamble for a whole range of reasons. Why do we gamble? Sensible gambling Some people say that there is no such thing as safe gambling. Keep away from high-risk forms of gambling where you can lose large sums of money very quickly. Limit the amount of time you gamble. This will give you time to do other, more important things with your life.

Limit the amount you spend to the amount you can afford to lose. When you have spent this much, walk away. Quit while you are ahead. If you continue, you are likely to lose because the odds are always stacked against you. That's how bookies and the casinos make their money. When gambling becomes a problem For most of us, gambling is a harmless activity. You may be a compulsive gambler if: you spend more money on gambling then you can afford.

If you continue to gamble, you could get into serious debt. You could also lose your home and your possessions you spend so much time gambling that you neglect other important areas of your life, like your family or your work. For example, you may become depressed when you lose or over-excited when you win. For example, you may lie to family and friends about your gambling activities or you may steal to fund your gambling habit.

Questions to ask yourself If you think you may have a gambling problem but are not sure, ask yourself: Is gambling making me unhappy at work or at home? Is gambling making it hard to sleep at night or concentrate during the day? Am I lying to other people and myself about how much I gamble? Am I gambling to get away from problems or worries? Am I borrowing money or selling possessions so that I can gamble?

If I have just won or just lost, do I feel I need to gamble just a little bit more? If you answered yes to any of these questions, then you may have a gambling problem. What causes compulsive gambling? Helping yourself If you feel that you have lost control of your gambling, there are some things you can do to help yourself.

Admitting you have a problem is the first and most important step. Find someone you can trust to talk to about your problem. Your task is to pin the probabilities back on the tree. Here are some clues to help you. Work out the levels. Try and work out the different levels of probability that you need. If you add together the probabilities for all of the branches that fork off from a common point, the sum should equal 1. They drew up a probability tree to show the probabilities, but in a sudden gust of wind they all fell off.

With this probability, you can make no assumptions about whether one of the events has already occurred. You have to find the probability of both events happening without making any assumptions. P A B is the probability of event A given event B. In other words, you make the assumption that event B has occurred, and you work out the probability of getting A under this assumption.

A: No, they refer to different probabilities. When you calculate P A B , you have to assume that event B has already happened. When you work out P A , you can make no such assumption. They look similar. P A B is the probability of getting event A given event B has already happened. P B A is the probability of getting event B given event A occurred. A: Both diagrams give you a way of visualizing probabilities, and both have their uses. It all depends what type of problem you need to solve.

Q: Is there a limit to how many sets of branches you can have on a probability tree? In practice you may find that a very large probability tree can become unwieldy, but you may still find it easier to draw a large probability tree than work through complex probabilities without it. Unfortunately, the ball landed in pocket 17, so you lose a few more chips. Maybe we can win some chips back with another bet. This time, the croupier says that the ball has landed in an even pocket. We can reuse the probability calculations we already did.

Our previous task was to figure out P Even Black , and we can use the probabilities we found solving that problem to calculate P Black Even. So how do we find P Black Even? All we need is some mechanism for finding these probabilities. Use the probabilities you have to calculate the probabilities you need. Take a look at the probability tree on the previous page. Take another look at the probability tree in So where does this get us? How do you think we can use it to find P Even?

The next step is to find the probability of the ball landing in an even pocket, P Even. We can find this by considering all the ways in which this could happen. These are all the possible ways in which a ball can land in an even pocket.

In other words, we add the probability of the pocket being both black and even to the probability of it being both red and even. The relevant branches are highlighted on the probability tree. Can you remember our original problem?

We wanted to find P Black Even where. Putting these together means that we can calculate P Black Even using probabilities from the probability tree. This means that we now have a way of finding new conditional probabilities using probabilities we already know—something that can help with more complicated probability problems. Imagine you have a probability tree showing events A and B like this, and assume you know the probability on each of the branches.

Now imagine you want to find P A B , and the information shown on the branches above is all the information that you have. How can you use the probabilities you have to work out P A B? To find P B , we use the same process that we used to find P Even earlier; we need to add together the probabilities of all the different ways in which the event we want can possibly happen.

There are two ways in which even B can occur: either with event A, or without it. This means that we can find P B using:. We can rewrite this in terms of the probabilities we already know from the probability tree. This means that we can use:. This is sometimes known as the Law of Total Probability , as it gives a way of finding the total probability of a particular event based on conditional probabilities.

We started off by wanting to find P A B based on probabilities we already know from a probability tree. What we need is a general expression for finding conditional probabilities that are the reverse of what we already know, in other words P A B.

And even though the formula is tricky, visualizing the problem can help. The Manic Mango games company is testing two brand-new games. Manic Mango selects one of the volunteers at random to ask if she enjoyed playing the game, and she says she did. If you have two events A and B, then. If you have n mutually exclusive and exhaustive events, A 1 through to A n , and B is another event, then. It will give you the same result, and it can keep you from losing track of which probability belongs to which event.

Did we make a mistake? This means that P Even Green is 0; therefore, it has no effect on the calculation. Is that always the case? They are two separate probabilities, and making this sort of assumption could actually cost you valuable points in a statistics exam.

For example, it can be used in computing as a way of filtering emails and detecting which ones are likely to be junk. Before you leave the roulette table, the croupier has offered you a great deal for your final bet, triple or nothing.

If you bet that the ball lands in a black pocket twice in a row, you could win back all of your chips. Notice that the probabilities for landing on two black pockets in a row are a bit different than they were in our probability tree in Bad luck!

Take a look at the equation for this probability:. For P Even Black , the probability of getting an even pocket is affected by the event of getting a black. We already know that the ball has landed in a black pocket, so we use this knowledge to work out the probability. We look at how many of the pockets are even out of all the black pockets.

To work out P Even , we look at how many pockets are even out of all the pockets. P Even Black gives a different result from P Even. In other words, the knowledge we have that the pocket is black changes the probability. These two events are said to be dependent. Look at the probability tree on the previous page again.

What do you notice about the sets of branches? Are the events for getting a black in the first game and getting a black in the second game dependent? Not all events are dependent. Sometimes events remain completely unaffected by each other, and the probability of an event occurring remains the same irrespective of whether the other event happens or not. What do you notice? These two probabilities have the same value.

In other words, the event of getting a black pocket in this game has no bearing on the probability of getting a black pocket in the next game. These events are independent. If one event occurs, the probability of the other occurring remains exactly the same. If events A and B are independent, then the probability of event A is unaffected by event B.

In other words. We can also use this as a test for independence. If A and B are mutually exclusive, then if event A occurs, event B cannot. In other words, if two events are independent, then you can work out the probability of getting both events A and B by multiplying their individual probabilities together. As the events are independent, the result is. If A and B are mutually exclusive, then if event A happens, B cannot.

Also, if event B happens, then A cannot. If A and B are independent, then the outcome of A has no effect on the outcome of B, and the outcome of B has no effect on the outcome of A. Their respective outcomes have no effect on each other. Q: Do both events have to be independent? Can one event be independent and the other dependent?

Q: Are all games on a roulette wheel independent? A: Yes, they are. Separate spins of the roulette wheel do not influence each other. In each game, the probabilities of the ball landing on a red, black, or green remain the same.

How do I use a Venn diagram to tell if events are independent? Venn diagrams are great if you need to examine intersections and show mutually exclusive events. The Case of the Two Classes. The Head First Health Club prides itself on its ability to find a class for everyone. As a result, it is extremely popular with both young and old. The Health Club is wondering how best to market its new yoga class, and the Head of Marketing wonders if someone who goes swimming is more likely to go to a yoga class.

The CEO disagrees. They ask a group of 96 people whether they go to the swimming or yoga classes. Out of these 96 people, 32 go to yoga and 72 go swimming. Are the yoga and swimming classes dependent or independent? Well, I hear you keep getting fledgling statisticians into trouble.

You want to work out the probability of getting two independent events? Just multiply the probabilities for the two events together and job done. With independent events, probabilities just turn out the same. I think that people need to think of me first instead of you; that would sort out all of these problems. By really thinking through whether events are dependent or not. Let me give you an example. Suppose you have a deck of 52 cards, and thirteen of them are diamonds.

What would be the probability of that happening? The events are dependent. You can no longer say there are 13 diamonds in a pack of 52 cards. Not fair, I assumed you put the first card back! That would have meant the probability of getting a diamond would have been the same as before, and I would have been right.

The events would have been independent. When people think about you first, it leads them towards making all sorts of inappropriate assumptions. Solved: The Case of the Two Classes. So how do we know the classes are independent? Here are a bunch of situations and events. Your task is to say which of these are dependent, and which are independent. Choosing a card from a deck of cards, putting the card back in the deck, and then choosing another one. Your task was to say which of these are dependent, and which are independent.

When you remove one sock, there are fewer socks to choose from the next time, and this affects the probability. Besides the chances of winning, you also need to know how much you stand to win in order to decide if the bet is worth the risk.

Betting on an event that has a very low probability may be worth it if the payoff is high enough to compensate you for the risk. Fred decides to throw a coin. I person eats alone if Fred and George go to the Diner. As these events are independent, this is equal to P 22 x P Skip to main content.

Head First Statistics by Dawn Griffiths. Start your free trial. Calculating Probabilities: Taking Chances. Roll up for roulette! Your very own roulette board. Note Just be careful with those scissors. Place your bets now! Brain Power What things do you need to think about before placing any roulette bets? What are the chances? Vital Statistics: Event An outcome or occurrence that has a probability assigned to it. Sharpen your pencil. Sharpen your pencil Solution. Find roulette probabilities.

You can visualize probabilities with a Venn diagram. Complementary events. BE the croupier Solution. Note The most likely event out of all these is that the ball will land in a black pocket. There are no Dumb Questions. Q: Q: Why do I need to know about probability? Q: Q: Are probabilities written as fractions, decimals, or percentages? A: A: They can be written as any of these. A: A: There certainly is. Q: Q: Do I always have to draw a Venn diagram? A: A: No. And the winning number is You can also add probabilities.

Vital Statistics: Probability To find the probability of an event A, use. Q: Q: It looks like there are three ways of dealing with this sort of probability. A: A: It all depends on your particular situation and what information you are given. Q: Q: If some events are so unlikely to happen, why do people bet on them? A: A: A lot depends on the sort of return that is being offered. Q: Q: Does adding probabilities together like that always work?

A: A: Think of this as a special case where it does. You win! Time for another bet. Note Uh oh! Different answers. Exclusive events and intersecting events. Brain Power What sort of effect do you think this intersection could have had on the probability? Problems at the intersection. Some more notation. Watch it! BE the probability Solution. Exercise Solution. A: A: Yes it is. Q: Q: Is there a limit on how many events can intersect? Another unlucky spin Conditions apply.

Find conditional probabilities. Note The probability of A give that we know B has happened. You can visualize conditional probabilities with a probability tree. Trees also help you calculate conditional probabilities. Handy hints for working with trees. Probability Magnets Solution. You can get coffee with or without donuts. Note Hint: maybe some of your other answers can help you.

If it makes you less sad, I'll move out of the state. You can keep to yourself. I'll keep out of your way. And if it makes you less sad, I'll take your pictures all down. Every picture you paint, I will paint myself out.

It's cold as a tomb, and it's dark in your room, when I sneak to your bed to pour salt in your wounds. So call it quits or get a grip. Say you wanted a solution. You just wanted to be missed. I'm only hoping as time goes, you can forget You are calm and reposed. Let your beauty unfold. Pale white, like the skin stretched over your bones. Spring keeps you ever close. You are second hand smoke. You are so fragile and thin.

Standing trial for your sins. Holding onto yourself the best you can. You are the smell before rain. You are the blood in my veins. My mom says all I have to do is smile at her and she forgets what I did to get in trouble. She feels her feet squish and remembers how upset her mom will be.

Her once bright white saddle shoes are now soaked and gray, and there is wetness climbing up her dress making it look murky brown. Betty feels her skin vibrating, radiating heat, and it spreads from her toes to the crest of her head, making her giggle.

After too long, Betty leaves his arms and surveys the boy in front of her. She smiles at his dark hair and blue-green eyes, and the crown on his head made of cardboard and colored in, probably by him and suddenly she just knows, can feel it with every fiber of her being.

Jughead nods, but looks sad. He smiles at her again and she feels her belly swoop. Betty steps forward and kisses him on the cheek before running away, not daring to look back at the boy who gave up his crown for her. What have you done? Betty grins and kicks her legs even though her mom is using a rag on her knees to get rid of the evidence.

And you know what? Alice replaces her yellow dress with a lilac one and tightens her pigtails. It was due to these births that the number once again surged during the nineties to early two-thousands due to the unlikeliness of having soulmates of their own… It is only telling what will happen when these unnatural children grow up whether the number will increase again…. At seven years old Betty stretches her neck to look out the car window to spot a gray beanie or a tuft of black hair and frowns when she sees nothing.

Betty jumps out of the car before her dad even has it turned off and grins when she sees Archie coming down his front steps. How was Montana? Betty shrugs. Well, a foal, and it was so cool. She let me and Polly name it! Archie starts bouncing his basketball again as they walk towards the hoop in his driveway. Betty rolls her eyes. I have to dig it out of my suitcase and I have stuff for Jug and Jellybean too.

She knocks incessantly on his front door, unable to stop herself. His mom opens the door, Jellybean on her hip. Immediately Jellybean starts kicking and babbling, wanting to be put down. Gladys reaches down with a small frown to pick up Jellybean, probably to keep her from running, the three-year-old is a firecracker.

Betty nods and heads back down the front steps to go around to the back of his house. What could be so wrong that it made Jughead exile himself to the treehouse and not come down, even for food? He adored Jellybean. His house was infinitely more fun than hers, Jellybean was always getting into something and his parents treated her as one of their own, she never waited for an invitation to come over, she just knew she was always welcome.

Betty hates how Polly teases her. Betty shields her eyes from the sun, pouting at the sight of the treehouse and how the rope ladder was pulled up. She crosses her arms the way her mom does when she means business. What happened? Betty climbs up as fast as she can. Her exuberance causes him to stumble, but he still holds onto her tightly. He holds her for a long moment, longer than she expected, and she pulls away to look at his face. Something is wrong so just tell me what it is.

Betty follows suit and tries not to notice how he moves away when their knees touch. He pulls out the brown leather wrist cuff, his fingers sliding over the embroidery. Are you okay? I thought it was a cute. Jughead sniffles and Betty watches as a fat tear rolls down his cheek. Even though he is so upset, being this close to him is the first time she felt peace in ten days.

It took a few minutes, but finally Jughead pulls away with a blush creeping up his neck. Betty just smiles at him, slipping his hat off his head to run her fingers through his unruly locks. Did your parents finally tell you where theirs are? You believe it too, right? She helps him snap it together and smiles again as he looks down at it fondly. Are you going to stay up here forever? Am I going to have to move in when we grow up?

Remember, they said it can feel funny to talk about. Talking about getting her first period was just not something she felt comfortable with. Who will keep Jellybean out of trouble? I need running water, Juggie. Jughead smiles at her, all warm and like before when he never doubted what they were to each other. Now, come on, we have to tell Jellybean her big brother is moving back home.

His mom comes out onto the back porch and looks down at her children with a knowing smile and winks at Betty, who nods back at her. Jughead steps back, shaking his head, and curling his fists together. I only ever see you in school, the most time I get with you is during recess, and even now all you want to do is hang out with Archie.

Betty nods and begins to stumble back away from him. By the time she was eleven, Jughead would be turning twelve less than two months later! She hates feeling so young. She was talking at ten months old, walking too, and her mom worked with her so much at home that she knew how to read before first grade even started.

They stay like that for a few minutes until everyone on the playground starts running towards some kind of commotion near the chain-link fence at the edge of the field. Jughead is in front of her, a bush still smoldering with the grass around it now black, with soot on his face. Betty feels as though her feet are glued to the ground.

Jughead started a fire? How, with what? Suddenly the teachers usher them back inside the school, but Archie and Betty both stand still. Then Jughead finally looks up at them, and Betty makes a move to rush forward. She looks back towards her soulmate and sees him walking away toward the police cars with the principal, his head twisting back to meet her eyes, silently pleading with her. He turns just in time to catch her in his arms. Ever since she was four years old, Jughead has always been there.

Being away from him makes her want to pull her hair out and rip her skin off. Jughead is being released, coming home to her, finally. They ask if they can come by the house after school, but his parents say they needed time to sort things out with him, to talk to him alone without a social worker or counselor, and she understands, she really does, but—she misses him so much that her bones hurt. So she finds herself tip-toeing around the neighborhood at three AM wrapped in a blanket instead of a jacket with a flashlight in her hand.

Betty uses the flashlight in his window, turning it off and on to get his attention. The sight makes her breath catch.

This is a way to protect against losses and manage them effectively. Again we can build on the maxDD we talked about earlier. You can write down the maxDD of each of the strategies you follow at the moment you start to follow it. If after starting to follow each strategy, one of them exceeds the historical maxDD you have noted, it would be advisable to stop following that strategy because you have entered a worse streak than any historical bad streak the strategy have had, and this may be a bad signal.

It is possible that it recovers and returns to have gains, but also it is possible not to, and by prudence, it might be better to stop following it. Practical recommendation: define a stop-loss policy that fits to your betting method and exercise a periodic control over your bets and strategies. In this way you will protect yourself against prolonged losses. Avoid losing bets with regular control! Another thing I wanted to comment on, Johnny, I know that you like soccer, what do you do when your team plays or when you have an intuition for a game?

Do you bet on your team or following your intuition? Serious error I told him. When you bet intuitively, viscerally, you have everything against you. You are not following any method or system, any recommendation, neither betting because of the result of a thorough analysis of the game in question. You are simply betting with the heart, without any basis, and this will end up leading you to ruin in the medium-long term.

Practical recommendation: analyze, choose and carefully select the strategies or recommendations that you will follow for your bets, and stick to it exclusively, never bet on intuition, because you will usually carry the odds against you. Avoid losing bets being disciplined! And to finish Johnny, I wanted to ask you, are you paying attention to the odds when you are betting, or are you just betting the pick away? Again, serious mistake! In bets you do not end up winning or losing because you are able to guess the future and win accordingly, obviously it is not like that.

In bets you will end up winning if the odds you play are favorable for you constant and consistently , or in other words, you will end up winning if you make your bets at good odds. Note that when a tipster recommends a pick, usually recommends at the same time a minimum odd, which according to his criteria, over this value the pick would be favorable for us.

Likewise, our strategy analysis tool, Betamin Builder , includes a minimum recommended odd for each pick. It is your decision if you bet below that odd or not; In fact, the results of the Betamin Builder strategies are registered without considering that minimum odd, but usually my recommendation is that you take care about the odds, not only the minimum, but also try to find the bookmaker that offers you the best possible odds.

Practical recommendation: do not ignore the value and meaning of the odds. Find the bookmaker that offers you the best possible odds. For this, you can work with several bookmakers and choose the one that interests you the most in each moment, or you can let an Asian bookmaker aggregator do the work for you and automatically offer you the best odds.

Nor do you ignore the meaning of the minimum recommended odds. Avoid losing bets selecting the best odds! In short Johnny, I hope I have helped you to avoid losing bets, and that you do better with your bets in the future.

In the end it is simply about being methodical, patient, disciplined, and having self-control , since it is usually the psychological factor that causes us to make mistakes. If we know how to detect them, we will be able to correct them. Always remember that luck does not come by itself, but comes as a result of hard work.

That said, good luck! Necessary cookies are absolutely essential for the website to function properly. This category only includes cookies that ensures basic functionalities and security features of the website. These cookies do not store any personal information. Any cookies that may not be particularly necessary for the website to function and is used specifically to collect user personal data via analytics, ads, other embedded contents are termed as non-necessary cookies.

It is mandatory to procure user consent prior to running these cookies on your website. The 5 mistakes that make you lose betting: what are they and how to avoid losing bets Share on Twitter. Share on Facebook. But the best of all is that you are in the right place to discover which are the most common failures that you should avoid.

Error number 1: not making a proper bank management The first thing I asked Johnny is to tell me about his bank management. Evaluate the risk of your strategies To help with this, I continued, there is a really important thing in the strategies generated with our strategy analysis tool Betamin Builder which is the maximum historical Draw Down maxDD.

Watch for hiking through the wilderness In fact, and this is important, when you flip a coin, the coin itself does not remember what came out in the previous roll, and the same result could continue to come out indefinitely.

At the end things are back to normal, take advantage of winning streaks What is happening to you is very easy to explain, and it has to do with the normalization of statistical data : you go through a bad streak, you lose and you abandon the strategy, and you change to a strategy that is in a good streak.

Discover 8 new profitable football betting systems based on Big Data clicking here!!! Error number 3: lack of control, absence of stop-loss As I was saying a moment ago, Johnny, you should keep a regular and routine control over your strategies and your bets.

Protect yourself against losses How to protect yourself? Error number 4: indiscipline Another thing I wanted to comment on, Johnny, I know that you like soccer, what do you do when your team plays or when you have an intuition for a game? Avoid losing bets following a system When you bet intuitively, viscerally, you have everything against you.

Error number 5: incorrect odds selection And to finish Johnny, I wanted to ask you, are you paying attention to the odds when you are betting, or are you just betting the pick away? Select your odds carefully Note that when a tipster recommends a pick, usually recommends at the same time a minimum odd, which according to his criteria, over this value the pick would be favorable for us.

In conclusion, how to avoid losing bets? Share on Twitter. Comments 2. It is really informative for sports betting.. Drinking meant having to get up in search of alcohol and Yoongi would rather stay where he was, next to Jimin. Why would you want to purposely make a hot mess of yourself?

His chest felt like it was on fire as he coughed. Without any more hesitation Yoongi took the cup from him and chugged it until there was nothing left. He set the empty cup back down on the table and leaned back to focus on taking deep breaths to try and even out his breathing. Once he sparked the lighter to life he took a deep breath and held the smoke in for a moment.

As he pulled the bowl away he tilted his head back and slowly exhaled. But as suddenly as the look had appeared, it was gone and Jimin leaned down to hand the bowl and lighter back to Kai. For a second Yoongi thought he had imagined it but then Jimin turned back to him, the corner of his lips quirked up into a smirk and Yoongi knew that Jimin was up to something. Yoongi pointedly ignored the brief look that Hoseok gave him, eyebrows raised in a silent question. Eventually Hoseok grew tired of constantly being dismissed or ignored and dropped it altogether but Yoongi had a sneaking suspicion there would be new questions for him tomorrow.

He let his head fall against the back of the couch with his exhale of smoke and let it rest there, eyes only somewhat glazed over as he stared up at the ceiling. He knew Jimin was teasing him. Jimin turned his lips down into a small pout that made Yoongi wish they were the only two in the room so he could pull Jimin in close and kiss the pout right off his face. Yoongi tried not to think about what it meant that he so desperately wanted to kiss Jimin--would deny anyone that tried to say he was addicted.

Without so much as a second glance back to everyone else, Jimin led Yoongi out the room, the beaded curtain danced behind them as they passed through to leave. There seemed to be more than when Yoongi first arrived, the air was heavy and the sheer amount of people made it difficult to breath or even hear himself think. Before they reached the end of the hall where Yoongi knew the kitchen was he was suddenly pushed into a room off to the side, the door clicked shut behind him. It took a second for Yoongi to realize that he had been shoved into the bathroom, the sound of music and people talking loudly was muffled by the door that had all but been slammed behind him.

He turned on his heel and came face to face with Jimin but before he could open his mouth to ask what he was doing there were suddenly a pair of lips crashing into his. Yoongi stumbled backwards and nearly tripped over his own feet at the suddenness of it. Yoongi walked Jimin backwards until the back of his legs bumped into the sink counter. Of all the times they had spent together getting high and making out it never went this far, never got this heated.

This was new territory. Somewhere along the way Yoongi had grown to want more more more, but never let himself dwell on it for the sake of their friendship. Yoongi breathed in deep through his nose, his mind was hazy with how much he wanted Jimin. When Jimin opened his eyes to look at Yoongi they were half-lidded, his lips slick with spit and his cheeks were tinted pink.

Briefly Yoongi wondered if he looked as wrecked as Jimin. He surged forward and caught those plush, thick lips into a bruising kiss. Yoongi found his mouth watering as he wondered what Jimin tasted like and his mouth acted before his brain could catch up and stop him.

He sighed at the contact, his eyebrows furrowed and mouth slack as he breathed heavily. Jimin groaned and tried his best to roll his hips into it but found it difficult to do with the way he sat on the edge of the counter. It was amusing and a bit fascinating just how impatient and needy Jimin had turned in the small amount of time they had been alone together.

Yoongi briefly wondered if he was always so responsive, so sensitive. Only one way to find out. Yoongi leaned forward, wrapped his lips around the spot of precome and gave a firm suck. There was the faint taste of salt and sex that only made Yoongi want Jimin more, made him want to sink his mouth down Jimin until he choked. Yoongi sucked and nibbled on the skin until it was red and purple with a dark bruise.

He took the head into his mouth, tongued at the slit and lapped up the precome that leaked from Jimin. Yoongi stroked him quickly, twisted his wrist on every upstroke and covered Jimin in his spit to make the glide easier as Yoongi took more and more of Jimin into his mouth. He wasted no time in building up a quick pace that made Jimin throw his head back with a low groan.

Having his mouth full of Jimin was better than Yoongi had imagined; he had more girth than Yoongi expected but if there was one thing Yoongi could brag about it was the way he could work his tongue and his mouth. Jimin unceremoniously thrusted his hips forward with a loud moan that fell from his lips.

Yoongi concentrated on breathing through his nose and how good it felt to be used by Jimin like this, to be the reason why Jimin groaned expletives under his breath with the approach of his orgasm. Jimin leaned against the counter, hands on either side of him, head tipped back while his chest rose and fell with his heavy breathing.

Yoongi used the back of his hand to wipe the spit from his chin and stood up on shaky legs. Yoongi could still hear the party going on strong on the other side of the door, the people oblivious to what was going on in the tiny frat house bathroom. A wave of relief washed over Yoongi and a groan slipped past his lips when Jimin rubbed the pad of his thumb against the slit.

Is that okay? Do you want to watch me bounce on your cock, hyung? He stroked Yoongi faster, more erratically. His orgasm hit him like a punch to the gut. As he attempted to even out his breathing Yoongi watched Jimin bring his hand up and lick it clean, eyes trained on Yoongi as he did so.

Jimin grinned cheekily at him, eyes upturned into crescents and Yoongi was taken aback by how he managed to look so sweet and adorable when he had just cleaned come off his hand by eating it. Once they were both tucked back into their jeans and did the best they could with the stains on their shirts Yoongi leaned across the sink to inspect his neck in the mirror. A fucking vampire? He was known for this kind of thing, now he just had the evidence of it marked onto his skin.

The hallway was less crowded than when they had escaped to the bathroom. How long had they been in there? They struggled to make it through the packed living room, bumped into people every which way they tried to go and nearly avoided the drunk girl by the dining room that almost spilled her drink on Yoongi. He turned to see Hoseok headed towards the both of them as he seemed to effortlessly slip past the crowd. From behind him Yoongi heard Jimin snort as he tried to hold back a laugh.

Once they slipped out the front door the cold night air hit them like a wall. Jimin pulled down the ends of the sleeves of his shirt to cover his hands completely. Jimin grinded down on the thigh Yoongi wedged between his legs, desperate to create some sort of friction. Jimin tugged on it until it broke free of his abuse, red and swollen. You can call me worse things than that. Yoongi raised his eyebrows but made a mental note to store that information for later. So he did. He felt hands run up his arms to come to rest in his hair, fingers tangled in the mess that had become of it.

And honestly, how was Yoongi supposed to say no with Jimin so needy underneath him? That look alone was enough to push Yoongi to finally sit back and hastily try to take his pants off. The cuff got caught on his ankle which sent Jimin into a fit of giggles he made no effort to hide.

Once Yoongi was finally free of his pants he leveled Jimin with a glare that silenced his giggling but the grin was still plastered on his face. Jimin was fully hard now, the wet patch on his boxer briefs bigger than it had been before back at the party.

He grabbed the closest lube--strawberry flavored--and a condom, and let them fall onto the bed next to his leg. Jimin had taken that moment to free himself of his underwear and laid completely naked underneath Yoongi, all smooth curves and firm muscles. Jimin, surprisingly, did as he was told without a snarky comment.

He turned his head so he could see Yoongi as best as he could, arms folded underneath his head, legs spread with hips just barely lifted. Jimin hummed with content just loud enough for Yoongi to hear and rolled his hips back. The smell of the lube hit Yoongi as soon as he popped the cap off the bottle and it only grew stronger when he slathered his fingers with it. At least it smelled nice enough, he figured. Jimin lifted his hips up until he could comfortably hold himself up on his knees, his shoulders pressed against the mattress as his hands came up to spread himself open for Yoongi.

But Yoongi knew they still had an important matter to take care of before he could do that. Despite the fact they both had already gotten off once, and that Yoongi normally took his time with his hookups to get the most out of them, both he and Jimin were far too impatient. Yoongi had thought of having Jimin splayed out underneath him a handful of times before, and although he had felt guilty thinking of his friend that way, it was always Jimin his mind wandered to whenever his hand found its way down his pants and around his dick.

After a few tentative thrusts and a pleased sound from Jimin, Yoongi quickly built the pace back up. Yoongi pulled his fingers out and shimmied out of his underwear. Yoongi held the base of his cock with one hand and stroked himself with the other hand with a low groan while Jimin threw a leg over his hips and lifted himself up.

He sank down until he was fully seated and Yoongi watched as his cock slowly disappeared inside of Jimin. It lacked finesse and a consistent flow but they were both too gone in the feeling of the other to care. It was mesmerizing.