A pair of dice is thrown 4 times. If getting a doublet is considered a success, find the probability of two successes.

.: Let $p$ be the probability of throwing doublet
$\{ (1,1),(2,2),(3,3),(4,4),(5,5),(6,6)\}$

with a pair of dice $= \cfrac{6}{{36}} = \cfrac{1}{6},$

then
$q = 1 - \cfrac{1}{6} = \cfrac{5}{6}$

$X$ has a binomial distribution with $n = 4,p = \cfrac{1}{6},q = \cfrac{5}{6}$

$\therefore$ Probability of getting 2 successes
$= P(X = 2){ = ^4}{C_2}{q^2}{p^2} = 6{\left( {\cfrac{5}{6}} \right)^2}{\left( {\cfrac{1}{6}} \right)^2} = \cfrac{{25}}{{216}}$