Question

What is the probability that two friends have different birthdays?
(a) $\frac{1}{365}$
(b) $\frac{2}{365}$
(c) $\frac{364}{365}$
(d) $\frac{363}{365}$

Answer 1

(c) $\frac{364}{365}$

Explanation:
One friend's birthday may fall on any one of the 365 days and the other friend's birthday may also fall on any one of the 365 days.
Total number of ways in which the birthdays of both the friends fall on particular days = (365 ⨯ 365)
The favourable outcomes for the event that both friends have the same birthday on any one of the 365 days = 365
∴ P( both have the same birthday) = $\frac{365}{\left(365\times 365\right)}=\frac{1}{365}$

∴ P( both have different birthdays) = 1- P( both have the same birthdays)
= $1-\left(\frac{1}{365}\right)=\frac{364}{365}$