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?
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 $\frac{1}{365}$
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