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What is the sample space for one spin of the roulette wheel? 1 All possible our comer {, 1, 2, , 36} b. Are the outcomes equally likely? Yes, they are equally.

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The wheel consist 38 spaces numbered 1 through 36, 0, and The sample space 'S' is defined as the all possible outcomes of the random experiment. So the.

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What is the sample space for one spin of the roulette wheel? 1 All possible our comer {, 1, 2, , 36} b. Are the outcomes equally likely? Yes, they are equally.

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To play a game, a metal ball is spun around the wheel and is allowed to fall into one of the numbered slots. a) What is the sample space? The sample space is.

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The wheel consist 38 spaces numbered 1 through 36, 0, and The sample space 'S' is defined as the all possible outcomes of the random experiment. So the.

Enjoy!

What is the sample space for one spin of the roulette wheel? 1 All possible our comer {, 1, 2, , 36} b. Are the outcomes equally likely? Yes, they are equally.

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4 If I spin a Roulette wheel, the sample space is {0,00, }. If I flip a coin 3 times, the sample space is {head, head, head (HHH), HHT, HTH, HTT, THH, THT.

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The wheel consist 38 spaces numbered 1 through 36, 0, and The sample space 'S' is defined as the all possible outcomes of the random experiment. So the.

Enjoy!

To play a game, a metal ball is spun around the wheel and is allowed to fall into one of the numbered slots. a) What is the sample space? The sample space is.

Enjoy!

4 If I spin a Roulette wheel, the sample space is {0,00, }. If I flip a coin 3 times, the sample space is {head, head, head (HHH), HHT, HTH, HTT, THH, THT.

Enjoy!

Probability theory can help you make predictions about your data and see patterns. All sorts of games are offered, from roulette to slot machines, poker to blackjack.

Life is full of uncertainty. The game is just beginning. One other thing to remember: if the ball lands on a green pocket, you lose.

On the previous page, we found that.

The important thing to remember is that a probability indicates a long-term trend only. This gives us. Which way is best? Is there a connection? 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. The two events are mutually exclusive, so no elements are shared between them. Want to give it a try? In stats-speak, an event is any occurrence that has a probability attached to it—in other words, an event is any outcome where you can say how likely it is to occur. You can place all sorts of bets with roulette. You can use it to help work out the probabilities in this chapter. Q: Does adding probabilities together like that always work? There are only three colors for the ball to land on: red, black, or green. It all depends on what kind of information you need to help you solve the problem. It can still be useful to double-check your results, though. 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. Suppose the only information you had about the roulette wheel was the probability of getting a green. Probability is measured on a scale of 0 to 1. It just so happens that today is your lucky day. Oh dear! Q: Do I always have to draw a Venn diagram? Finally, use your roulette board to count all the holes that are either black or even, then divide by the total number of holes. This sort of diagram is known as a Venn diagram. When we added the two probabilities together, we counted the probability of getting a black and even pocket twice. Sound easy enough? It can help you make sense of apparent randomness. A: Think of this as a special case where it does. A: A lot depends on the sort of return that is being offered. What about the black and even events? Maybe some bets are more likely than others. Here are all the possible outcomes from spinning the roulette wheel. Have you cut out your roulette board? The two events intersect. Instead of numbers, you have the option of using the actual probabilities of each event in the diagram. I thought I was learning about statistics. To work out the probability of getting a 7, take your answer to question 2 and divide it by your answer to question 1. In set theory, the possibility space is equivalent to the set of all possible outcomes, and a possible event forms a subset of this. Q: Are probabilities written as fractions, decimals, or percentages? Go on—you know you want to. A I is known as the complementary event of A. To get the correct answer, we need to subtract the probability of getting both black and even. The main pockets are numbered from 1 to 36, and each pocket is colored either red or black. 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. Sometimes it can be impossible to say what will happen from one minute to the next. Q: Why do I need to know about probability? Q: It looks like there are three ways of dealing with this sort of probability. Calculating the probability of getting a black or even went wrong because we included black and even pockets twice. A: No. First of all, we found the probability of getting a black pocket and the probability of getting an even number. 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. Q: Can anything be in both events A and A I? It includes all of the elements in A and also those in B. There are two extra pockets numbered 0 and These pockets are both green. Where do you think the ball will land? 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. Between them, they make up the whole of S. It sounds like we need to look at some probabilities What things do you need to think about before placing any roulette bets? Probability is a way of measuring the chance of something happening. Q: If some events are so unlikely to happen, why do people bet on them? 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. For each event you should have written down the probability of a successful outcome. Mark the probability on the scale below. Probability lets you predict the future by assessing how likely outcomes are, and knowing what could happen helps you make informed decisions. An outcome or occurrence that has a probability assigned to it. 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. Given the choice, what sort of bet would you make? 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. This event is actually impossible—there is no pocket labeled Therefore, the probability is 0. You had to work out a probability for roulette, the probability of the ball landing on 7. Even though our most likely probability was that the ball would land in a black pocket, it actually landed in the green 0 pocket. A lot of statistics has its origins in probability theory, so knowing probability will take your statistics skills to the next level. Take a look at your roulette board. If two events are mutually exclusive, only one of the two can occur. What do you get? A: There certainly is. 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:. Look at the events on the previous page. People are tempted to make bets where the return is high, even though the chances of them winning is negligible. If an event is impossible, it has a probability of 0. For instance, you can bet on a particular number, whether that number is odd or even, or the color of the pocket. Possible events are all subsets of S. For each event below, write down the probability of a successful outcome. Try the exercise on the next page, and see what happens. S is known as the possibility space , or sample space. In general, the less likely the event is to occur, the higher the payoff when it happens. They exhaust all possibilities. You lose some of your chips. A: It all depends on your particular situation and what information you are given. A: They can be written as any of these.