The birthday paradox
Asked at Jane Street, SIG, IMC
People enter a room one by one. Assume birthdays are independent and uniformly distributed over 365 days (ignore leap years and twins).
How many people must be present before the probability that at least two share a birthday exceeds 50%?
Most people guess a number close to 183, the true answer is far smaller.
Show a hint
Computing "at least one shared birthday" directly is messy. Compute the probability that all birthdays are distinct and subtract from 1.