A pair of dice is thrown 4 times. If getting a doublet is considered a success, find the probability distribution of number of successes. Also, find the mean and variance of number of successes.

Explanation

Total outcomes=36

Probability of success=P=6/36=1/6

Probability of failure=Q=30/36=5/6

X=no. of times we get a doublet

`P(x=0)=4C_0(1/6)^0(5/6)^4=625/1296`

`P(x=1)=4C_1(1/6)^1(5/6)^3=500/1296`

`P(x=2)=4C_2(1/6)^2(5/6)^2=150/1296`

`P(x=3)=4C_3(1/6)^3(5/6)^1=20/1296`

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