Question

You go to a party with 500 guests. What is the probability that exactly one other guest has the same birthday as you? (Assume no one has a birthday on Feb 29).

Answer 1

0.3486 or 34.86%

Explanation:

For each guest, the probability that they share a birthday with you is 1 in 365. Aside from you, there are 499 guests.

Therefore, this problem can be modeled by a binomial probability model with probability of success 1/365.

The probability of exactly 1 success in 499 trials is given by:

`P(x=1) = (499!)/((499-1)!)*{(1)/(365)} ^1*{(364)/(365)} ^(498)\\P(x=1) =0.3486 = 34.86\%`

There is a 0.3486 or 34.86% chance that exactly one other guest has the same birthday as you.