Question

A bag contain $4$ red, $5$ blue and $3$ green balls if two ball are drawn at random What is the probability that both are red?

Answer 1

Given $4$ red,$5$ blue,$3$ green balls

Total possible outcomes(selecting 2 out of 12(4+5+3) balls ) ${=}^{12}{C}_2=\frac{12\times 11}{2\times 1}=66$

Favourable outcomes(selecting 2 out of 4 red balls) ${=}^4{C}_2=\frac{4\times 3}{2\times 1}=6$

$P\left(E\right)=\frac{6}{66}=\frac{1}{11}$