Find the probability distribution of the number of doublets in four throws of a pair of dice. Also find the mean and variance of this distribution.

Explanation

Here X = number of doublets. Possible doublets are `(1,1),(2,2),(3,3),(4,4),(5,5),(6,6)`


Where , the dice thrown trice, `therefore X` take the value `0,1,2, or 3 .`


Probability of doublet `=p=frac{1}{6} and q=1-frac{1}{6}=frac{5}{6}`


`
P(0)=P`( no doublet )`=q q q=frac{5}{6} times frac{5}{6} times frac{5}{6}=frac{125}{216}`




`P(1)=P text { (one doublet })=p q q+q p q+q q p `


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