Question

In a room full of 50 people, what is the probability that at least two people have the same birthday? Assume that all birthdays are equally likely (uniform distribution) and there are 365 days in the year.


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Answer 1

The correct answer is 0.970(approximately).

Given: Number of people = 50

To Find: Probability that at least two people have the birthday on same day.

Solution:

Probability that at least two people have the birthday on same day = 1 - (Probability that all are born on different days).

So, the required probability is

=  $1-\frac{365*364*363.....*316}{365*365*365.....*365}$

= $\frac{365!}{315!*365^{50} }$

= 0.970 approximately.

Hence, the answer is 0.970(approx.).

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