Mathematics: What is the probability that at least 2 students in a class of 36 have the same birthday?

You need to combine like terms. So it would be 14x....

What is the probability that at least 2 students

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nicpinela1234

14.03.2022

Given a group of n students, and given the fact that there are 365 days in one year, the probability that there are no students with the same birthday is given by
$p_{no} (n) = \frac{364}{365} \cdot \frac{363}{365} \cdot ... \cdot \frac{365-n+1}{365} = \frac{364!}{365^{n-1} (365-n)!}$
Therefore, the probabilty that there are at least 2 students with same birthday is the complementary of this value:
$p_{yes} (n) = 1 -p_{no}(n) =1- \frac{364!}{365^{n-1} (365-n)!}$

And if we use n=36 (number of students), we find
$p=1- \frac{364!}{365^{36-1} (365-36)!} \sim 0.83$
So, the probability that there are at least 2 students in a group of 36 with same birthday is approximately 83%.

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What is the probability that at least 2 students in a class of 36 have the same birthday?

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