Question

A bag contains $6$ white and $4$ black balls .$2$ balls are drawn at random. Find the probability that they are of same colour.

Answer 1

Let $S$ be the sample space

Then $n\left(S\right)=$ number of ways of drawing $2$ balls out of $(6+4)=10$

${\Rightarrow }^{10}{C}_2=\frac{10\times 9}{2\times 1}=45$

Let $E=$ event of getting both balls of same color

Then,$n\left(E\right)=$ no of ways ($2$ balls out of six) or ($2$ balls out of $4$)

${=}^6{C}_2{+}^4{C}_2$

$=\frac{6\times 5}{2\times 1}+\frac{4\times 3}{2\times 1}=15+6=21$

$\therefore P\left(E\right)=\frac{n\left(E\right)}{n\left(S\right)}=\frac{21}{45}=\frac{7}{15}$