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

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Aicharya · Accepted Answer

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

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

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