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

Explanation

`P(S=0)=5/6*5/6*5/6`

`P(S=1)=3C_1*5/6*5/6*5/6`

`P(S=2)=3c_2*5/6*1/6*1/6`

`P(S=3)=1/6*1/6*1/6`

Mean=`sumP(6)S`

`=P(s=0)*0+P(s=1)*1+P(s=2)*8+P(s=3)*3`

`=0+(3*5*5)/(6*6*6)+(3*5*1*2)/(6*6*6)+(3*1)/(6*6*6)`

`(75+30+3)/(216)=108/216=1/2`