Two dice are thrown simultaneously. If \(\mathrm{X}\) denotes the number of sixes, then the expectation of \(\mathrm{X}\) is

Probability of getting \(6=\frac{1}{6}\)
\(\mathrm{X}\) denotes number of times of getting 6 , So \(\mathrm{x}\) can take values \(0,1,2\).
\(\begin{aligned}
\mathrm{P}(\mathrm{x} & =0)=\frac{5}{6} \times \frac{5}{6}=\frac{25}{36} \\
\mathrm{P}(\mathrm{x} & =1)=\left(\frac{1}{6} \times \frac{5}{6}\right)+\left(\frac{5}{6} \times \frac{1}{6}\right)=\frac{10}{36} \\
\mathrm{P}(\mathrm{x} & =2)=\frac{1}{6} \times \frac{1}{6}=\frac{1}{36} \\
\mathrm{E}(\mathrm{x}) & =\sum \mathrm{p}_{\mathrm{i}} \mathrm{x}_{\mathrm{i}}\end{aligned}\)
\(=\left(\frac{25}{36}\right)(0)+\left(\frac{10}{36}\right)(1)+\left(\frac{1}{36}\right)(2)=\frac{10+2}{36}=\frac{1}{3}\)