Question

There are three boys and two girls. A committee of two is to be formed. Find the probability of event that the committee contains at least one girl

Answer 1

Given 3 boys and 2 girls

Selecting two of the five $\left(n\right(S\left)\right)={}^5{C}_2$

$\therefore n\left(S\right)=\frac{5!}{2!\cdot 3!}=10$

$A=$ at least one girl

$A=\left\{\right(b_1,G_1),(b_2,G_1),(b_3,G_1\left)\right(b_1,G_2),(b_2,G_2),(b_3,G_2),(G_1,G_2\left)\right\}$

$\therefore n\left(A\right)=7$

$\therefore P\left(A\right)=\frac{n\left(A\right)}{n\left(S\right)}=\frac{7}{10}$