# Probability: Birthdays on the Same Day

Determine the number of people needed to ensure that the probability at least two of them have the same day of the year as their birthday is at least 70 percent, at least 80 percent, at 90 percent, 95 percent, at least 98 percent, and at least 99 percent.

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#### Solution Preview

Let's say the number of people needed to meet the probability is N. We will also assume that a year has 365 days (no leap years!).

The easiest way to think about it is to find the probability that NO two people have the same birthday. Then the probability that AT LEAST two people have the same birthday will be 1- (probability that NO two people have the same birthday).

We fix 'N' and determine the probability that no two people, in a room of N people, have the same birthday. Say that the people are

P(1),P(2),...,P(N). Now person P(1) may have any of the 365 days of the year for his birthday without contradicting the condition that no two people in the room will have the same birthday i.e. the ...

#### Solution Summary

The probablities of people having ths same birthday are investigated using permutations.