# What is the probability that in a group of two people, both

Question:

What is the probability that in a group of two people, both will have the same birthday, assuming that there are 365 days in a year and no one has his/her birthday on 29th February?

Solution:

We know that,

Probability of occurring $=1$ - the probability of not occurring

Let's calculate for the probability of not occurring, i.e. probability such that both of them don't have a birthday on the same day. For suppose the first person has a birthday on a particular day then the other person can have a birthday in the remaining 364 days

Probability of not having the same birthday

$=\frac{364}{365}$

Probability of having same birthday $=1$ - probability of not having the same

Birthday

$=1-\frac{364}{365}$

$=\frac{1}{365}$

Conclusion: Probability of two persons having the same birthday is $\frac{1}{365}$