x 2 3 1 1 3 2 6 27 2 9 2 HHT HTH THH 3 C 32 x 2 3 2 1 3 1 12 27 4 9 3 HHH 1 C

# X 2 3 1 1 3 2 6 27 2 9 2 hht hth thh 3 c 32 x 2 3 2 1

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Hypergeometric probability distributionsWith the binomial distribution, the probability of success did not change with each successive trial. For example, when you roll a 6-sided dice, the probability of rolling a 1 is always 1 over 6 (or approximately 16.7%). However, there are many instances where the probability of a particular outcome changes as each object is selected from a given amount. With the binomial probability distribution, we are sampling with replacement, so p and q stay constant. When you have sampling without replacement, the chance of a success or failure changes from trial to trial. This type of scenario is called a hypergeometric probability distribution. In this case, the outcome of an experiment is still either a success or a failure, but the trials are dependent on one another. If you start with a population of N items, and during an experiment you sample n items from the population, the probability of selecting items with a particular characteristic will change as each item is selected from the population (and not replaced). ExampleA cookie jar contains 5 chocolate chip cookies and 4 peanut butter cookies. Suppose you reach into the cookie jar (without looking) and select 3 cookies, oneat a time, without replacement. a. Create a tree diagram to model all of the possible outcomes of this experiment.

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