๐ŸŽฐ 4. Calculating Probabilities: Taking Chances - Head First Statistics [Book]

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Remember to stay realistic about the long odds on this popular game of chance. Approach roulette with the sober realization that, with a house advantage of While working on his doctorate at the University of Oregon, he learned how to.


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For the most part, calculating roulette payouts is just a matter of multiplication. Each bet pays out at certain odds, and that determines what you.


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THE PROBABILITY EQUATION. Here is the principal mathematical formula for calculating the chance of any roulette outcome or event. First we.


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Press a button below where the ball lands Red Black Odds Evens โ€‹ Straight Split Street Square Six Line. CalculationsCalculate the roulette.


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You had to work out a probability for roulette, the probability of the ball landing on 7. Here's how you calculate the solution, step by step. image with no caption.


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Probability of a Roulette Wheel

You can place all sorts of bets with roulette. This event is actually impossibleโ€”there is no pocket labeled Therefore, the probability is 0. All sorts of games are offered, from roulette to slot machines, poker to blackjack. Sometimes it can be impossible to say what will happen from one minute to the next. Which way is best? It can help you make sense of apparent randomness. The important thing to remember is that a probability indicates a long-term trend only. You had to work out a probability for roulette, the probability of the ball landing on 7.

Life is full of uncertainty. They exhaust all possibilities. Try the exercise on the next page, and see what happens. If how to work out roulette odds event is impossible, it has a probability of 0. Is there a connection? A lot of statistics has its origins in probability theory, so knowing probability will take your statistics skills to the next level.

A: They can be written as any of these. To work out the probability of getting a 7, take your answer to question 2 and divide it by your answer to question 1. This gives us. In this case, adding the probabilities gives exactly the same result as counting all the red or black pockets and dividing by To find the probability of an event A, use.

For each event you should have written down the probability of a successful outcome. For each event below, write down the probability of a successful outcome. This sort of diagram is known as a Venn diagram. Here are all the possible outcomes from spinning the how to work out roulette odds wheel.

Sound easy enough? On the previous page, we found that.

In general, the less likely the event is to occur, the higher the payoff when it happens. For instance, you can bet on a particular number, whether that number is odd or even, or the color of the pocket. Oh dear! Mark the probability on the scale below. The two events are mutually exclusive, so no elements are shared between them. To get the correct answer, we need to subtract the probability of getting both black and even. It all depends on what kind of information you need to help you solve the problem. There are two extra pockets numbered 0 and These pockets are both green. Q: Why do I need to know about probability? Calculating the probability of getting a black or even went wrong because we included black and even pockets twice. Probability lets you predict the future by assessing how likely outcomes are, and knowing what could happen helps you make informed decisions. It includes all of the elements in A and also those in B. There are only three colors for the ball to land on: red, black, or green. One other thing to remember: if the ball lands on a green pocket, you lose. To find the probability of winning, we take the number of ways of winning the bet and divide by the number of possible outcomes like this:. Even though our most likely probability was that the ball would land in a black pocket, it actually landed in the green 0 pocket. I thought I was learning about statistics. Have you cut out your roulette board? People are tempted to make bets where the return is high, even though the chances of them winning is negligible. The croupier spins a roulette wheel, then spins a ball in the opposite direction, and you place bets on where you think the ball will land. Go onโ€”you know you want to. Suppose the only information you had about the roulette wheel was the probability of getting a green. Calculate the probability of getting a black or a red by counting how many pockets are black or red and dividing by the number of pockets. What do you get? Q: If some events are so unlikely to happen, why do people bet on them? When we added the two probabilities together, we counted the probability of getting a black and even pocket twice. Maybe some bets are more likely than others. If two events are mutually exclusive, only one of the two can occur. In stats-speak, an event is any occurrence that has a probability attached to itโ€”in other words, an event is any outcome where you can say how likely it is to occur. In set theory, the possibility space is equivalent to the set of all possible outcomes, and a possible event forms a subset of this. It just so happens that today is your lucky day. Instead of numbers, you have the option of using the actual probabilities of each event in the diagram. Probability is measured on a scale of 0 to 1. You lose some of your chips. Between them, they make up the whole of S. Q: Does adding probabilities together like that always work? We might not be able to count on being able to do this probability calculation in quite the same way as the previous one. One way of doing so is to draw a box representing the possibility space S , and then draw circles for each relevant event. A: It all depends on your particular situation and what information you are given. If we know P Black and P Red , we can find the probability of getting a black or red by adding these two probabilities together. Q: Can anything be in both events A and A I? A: Think of this as a special case where it does. To work out the probability, all we have to do is count how many pockets are red or black, then divide by the number of pockets. A: No. When we were working out the probability of the ball landing in a black or red pocket, we were dealing with two separate events, the ball landing in a black pocket and the ball landing in a red pocket. Possible events are all subsets of S. The main pockets are numbered from 1 to 36, and each pocket is colored either red or black. It can still be useful to double-check your results, though. Q: Are probabilities written as fractions, decimals, or percentages? The two events intersect. What about the black and even events? Finally, use your roulette board to count all the holes that are either black or even, then divide by the total number of holes. Given the choice, what sort of bet would you make? Q: It looks like there are three ways of dealing with this sort of probability. A: There certainly is. Look at the events on the previous page. First of all, we found the probability of getting a black pocket and the probability of getting an even number. Probability is a way of measuring the chance of something happening. S is known as the possibility space , or sample space. Want to give it a try? It sounds like we need to look at some probabilities What things do you need to think about before placing any roulette bets? An outcome or occurrence that has a probability assigned to it. Where do you think the ball will land? The game is just beginning. If you know how likely the ball is to land on a particular number or color, you have some way of judging whether or not you should place a particular bet. You can use it to help work out the probabilities in this chapter. A I is known as the complementary event of A. A: A lot depends on the sort of return that is being offered. Q: Do I always have to draw a Venn diagram? Probability theory can help you make predictions about your data and see patterns. Take a look at your roulette board.