Consider a group of kk people. Assume that each person's birthday is drawn uniformly at random from the 365 possibilities. (And ignore leap years.) What is the smallest value of kk such that the expected number of pairs of distinct people with the same birthday is at least one?

Question

Mathematics

Phoenix Abbott

23 August, 02:43

Consider a group of kk people. Assume that each person's birthday is drawn uniformly at random from the 365 possibilities. (And ignore leap years.) What is the smallest value of kk such that the expected number of pairs of distinct people with the same birthday is at least one?

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Answers (1)

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Noe Golden · Answer 1

366

Step-by-step explanation:

Since there are 365 possible slots for people to have their birthday on, the worst case happens when all 365 people have different birthday. This means the 366th person would have their birthday falls on any of other's birthday. Hence, kk must be at least 366.