Exercise 3.1

Answers

If the k-th person’s arrival results in the first birthday match, the first k − 1 people have 365 ∗ 364 ∗⋯ ∗ (365 − k + 2) choices of birthday assignments such that no two people have the same birthday. The k-th person has k − 1 choices of birthdays, since their birthday must match that of one of the first k − 1 people.

Thus,

P(X = k) = 365 ∗ 364 ∗⋯ ∗ (365 − k + 2) 365k−1 k − 1 365

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2021-12-05 00:00
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