Question

Savita and Hamida are friends. Find the probability that both of them have same birthday.

Answer 1

Finding probability of having different birthday,

Selecting $2$ days out of $365$ in ${}^{365}{C}_2$ ways

Total choices $=365\times 365$

$\Rightarrow$ Probability $=\frac{{}^{365}{C}_2}{(365{)}^2}=\frac{365\times 364}{2\times (365{)}^2}=\frac{182}{365}$

$\Rightarrow$ Required probability $=1-\frac{182}{365}=\frac{163}{365}$.