Question

A pair of dice is thrown $4$ times. If getting a total of $9$ in a single throw is considered as a success then find the mean and variance of successes.

Answer 1

$P=$probability of getting a total of $9=\frac{4}{36}=\frac{1}{9}$
$\therefore$ $1-\frac{1}{9}=\frac{8}{9}$
$\therefore$ mean$=np=4\times \frac{1}{9}=\frac{4}{9}$
variance$=npq=4\times \frac{1}{9}\times \frac{8}{9}=\frac{32}{81}$