Find the probability distribution of the number of sixes in three tosses of a die.

Explanation

Let `X ` be the number of `6` in `3` tosses of a die.

Then `X` follows a binomial distribution with `n=3.`

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

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

`P(X=0)=^{3} C_{0}(frac{1}{6})^{0}(frac{5}{6})^{3}`

`P(X=1)=^{3} C_{1}(frac{1}{6})^{1}(frac{5}{6})^{3-1}`

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

`P(X=3)=^{3} C_{3}(frac{1}{6})^{3}(frac{5}{6})^{3-3}`
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