Question

A pair of dice is thrown $5$ times. Find the probability of getting a doublet twice.

Answer 1

In a single throw of a pair of dice probability of getting a doublet is $\frac{1}{6}$
considering it to be a success, $p=\frac{1}{6}$
$\therefore$ $q=1-\frac{1}{6}=\frac{5}{6}$
number of success $r=2$
$\therefore$ $P(r=2){=}^5{\text{C}}_2{p}^2{q}^3=10.{\left(\frac{1}{6}\right)}^2.{\left(\frac{5}{6}\right)}^3=\frac{625}{3888}$