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

1.	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?
Answer» 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 \(\frac{1}{365}\)

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?

Answer»

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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