I have the following problem. It is a simple birthday probability problem with 3 people but I can't crack it
Annie, Boris, and Charlie have random and independent birthdays. (We ignore leap years,
so that a year has 365 days.) What is the probability that Annie, Boris, and Charlie have
the same birthday?
My attempt is to take the probability that 2 of them have the same birthday and multiply it by 3, because there are three people but this does not seem to be right.
Best Answer
To solve this problem, take it step by step.
What is the probability of Annie having a birthday on a particular day of the year:
1/365What is the probability of Boris having a birthday on the same day =
(1/365) * (1/365)Similarly, probability of Charlie having a birthday on the same day =
(1/365)^3The above answer is for a specific day in a year. Since we are fine with any day in the year, multiply the answer with 365 (total number of days in the year).
So, probability of all three having a birthday on the same day in the year =
(1/365)^2