Three people, one birthday

Topic: Random experiments and probability · more questions on this topic
‹ A point drawn from the unit interval One of each court card ›

Three people are drawn from a large population, so that their birthdays are independent and uniform on 365 days. Find the probability that all three birthdays coincide.

Worked answer (click to show)

The first birthday is free. Each of the other two matches it with probability 1/365. The probability is 1/365^2, the same count as three identical labels drawn with replacement from 365 labels.