What is the probability that in a group of (i)2 people, both will have the same birth-day? (ii)3 people, at least two will have the same birth-day? Assuming that there are 365 days in a year and no one has his/her birth day on 29th February.

Explanation

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 = `364/365`

`364/365`

Probability of having same birthday

= 1 – probability of not having the same Birthday = `1 − 364/365`
`1−364/365 = 1/365`

Conclusion: Probability of two persons having the same birthday is `1/36`