Question

A pair of dice is thrown $4$ times. If 'getting a doublet' is considered a success, then find the probability of atleast $2$ successes.

Answer 1

Total numbe of outcomes $36$

$p=\frac{6}{36}=\frac{1}{6}$

$q=1-p=1-\frac{1}{6}=\frac{5}{6}$

$P(X=2){=}^4{C}_2{p}^2{q}^2$

$=6{\left(\frac{1}{6}\right)}^2{\left(\frac{5}{6}\right)}^2$

$=\frac{150}{1296}$