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

Explanation

In this question, X represents the number of sixes obtained when two dice are thrown simultaneously. Therefore, {X} can take the value of 0,1 , or 2 .

therefore {P}({X}=0)={P} (notgettingsixonanyofthedice )`=frac{25}{36}`

P(X=1)=P( sixonfirstdieandnosixonseconddie )+
P (nosixonfirstdieandsixonseconddie)


`=2(frac{1}{6} times frac{5}{6})=frac{10}{36}`


P(X=2)=P( sixonboththedice )`=frac{1}{36}`

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