461.Position in the Sundae Line
★★★combinatoricsCh. 2 — Axiomatic and Conditional Probability444+ Problems in Probability
An ice-cream shop will give a free sundae to the first person in line whose birthday matches that of someone who already bought ice cream ahead of them. Birthdays are uniform over 365 days and you know nobody else's birthday. Which position in line should you choose to maximize the probability that you win the sundae?
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You win at position if the first birthdays are all distinct and yours matches one of them. Compare consecutive positions.
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