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  • Two dice are thrown simultaneously. If X denotes the number of sixes, find the expectation of X.

Q.11    Two dice are thrown simultaneously. If X denotes the number of sixes, find the expectation of X.

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X denotes the number of sixes, when two dice are thrown simultaneously.

X can be 0,1,2.

\therefore    Not getting six on dice P(X)=\frac{25}{36}

       Getting six on one time when  thrown twice : P(X=1)=2\times \frac{5}{6}\times \frac{1}{6}=\frac{10}{36}

        Getting six on both dice : P(X=2)= \frac{1}{36}=\frac{1}{36}

X 0 1 2
P(X) \frac{25}{36} \frac{10}{36} \frac{1}{36}

Expectation of X = E(X)

                        E(X)=0\times \frac{25}{36}+1\times \frac{10}{36}+2\times \frac{1}{36}

                         E(X)= \frac{12}{36}

                         E(X)= \frac{1}{3}

Posted by

seema garhwal

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