We get this by letting say b j be the event that

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We get this by letting, say, B j be the event that person j shares k ’s birthday, so P B j 1/365. We want P B 1 B 2 ... B k 1 1 P  B 1 B 2 ... B k 1 c 1 P B 1 c B 2 c ... B k 1 c 1 P B 1 c P B 2 c  P B k 1 c 1 364 365 364 365 364 365 Even when k 100, this probability is only about .238. 112
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EXERCISE: What is the smallest (integer) k such that the probability that someone in a randomly compiled group shares your birthday is at least .5? (Hint: You need to find k such that 1 364 365 k 1 .5 or 365 364 k 1 2. It might help to use logarithms.) 113
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