Question

A dice is thrown thrice. A success is 1 or 6 in a throw. Find the mean and variance of the number of successes.

Answer 1

Here, n =3
$$\begin{gathered} p\mathit{}=\mathrm{probability}\mathrm{of}\mathrm{getting}1\mathrm{or}6=\frac{1}{3} \\ \text{and}q=1-\frac{1}{3}=\frac{2}{3} \\ \mathrm{Mean}=\mathit{}np=1 \\ \mathrm{Variance}=\mathit{}npq=\frac{2}{3} \end{gathered}$$