An urn contains 3 white and 6 red balls. Four balls are drawn one by one with replacement from the urn. Find the probability  distribution of the number of red balls drawn. Also find mean and variance of the distribution.

Explanation

There are total 9 balls

Success:drawing a red ball.

`n=4,P=6/9=2/3,q=1/3`

P(r red balls)=P(X=r)

`=nC_rP^rQ^(n-r)=4C_r(2/3)^r(1/3)^(4-r)`

`=4C_r*2^r/3^4`

Mean=`sumx_iP_i`

`=0+8/81+(2*24)/81+(3*32)/81+(4*16)/81`

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