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elemprob-page5

# elemprob-page5 - one of so the answer is 4 4 13 12 4 1 52 5...

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one of, so the answer is 13 · 12 4 4 4 1 52 5 . Example. What is the probability that in a poker hand we get exactly 3 of a kind (and he other two cards are of different ranks)? Answer. The probability of 3 aces, 1 king and 1 queen is 4 3 4 1 4 1 52 5 . We have 13 choices for the rank we have 3 of and 12 2 choices for the other two ranks, so the answer is 13 12 2 4 3 4 1 4 1 52 5 . Example. In a class of 30 people, what is the probability everyone has a different birthday? (We assume each day is equally likely.) Answer. Let the first person have a birthday on some day. The probability that the second person has a different birthday will be 364 365 . The probability that the third person has a different birthday from the first two people is 363 365 . So the answer is 1 - 364 365 363 365 · · · 336 365 . Example. Suppose 10 people put a key into a hat and then withdraw one randomly. What is the probability at least one person gets his/her own key? Answer. If E i is the event that the i th person gets his/her own key, we want
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