Savita and Hamida are friends. What is the probability that both will have (i) different birthdays? (ii) the same birthday? (ignoring a leap year).

Solution: Let Savita birthday is on $x$ day.
(i) Then, for Hamida having different birthday, there can be other $364$ days(other than x) as there are $365$ days in a year.
So, probability of having them different birthdays = $\frac{364}{365}$

(ii) For having same birthday, Hamida birthday should also be on day $x$.
So, there is only single possibility of them having same birthday.
So, probability of having them same birthdays = $\frac{1}{365}$