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

Let `p` denote the probability of getting a doublet in a single throw of a pair of dice. Then


`p=frac{6}{36}=frac{1}{6}`


Therefore, `q=1-p=1-frac{1}{6}=frac{5}{6}`

Let `X` denote the number of doublets in four throws of a pair of dice. Clearly, `X` has the binomial distribution with ` n=4, p=frac{1}{6} and q=frac{5}{6}`.

`therefore P(X=r)=^{4} C_{r}(frac{5}{6})^{4-r}(frac{1}{6})^{r}` where `r=0,1,2,3 and 4`


...