If 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

Let ` X` be the number of times a doublet is obtained in four throws.

Then, `p=` probability of success in one throw of a pair of dice `=
frac{6}{36}=frac{1}{6}`

`and q=frac{5}{6} ; n=4`

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

As `{n}=4 and p=frac{1}{6}`,

mean `=n p=frac{4}{6}=frac{2}{3}`

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

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