If for a binomial distribution `P(X=1)=P(X=2)=alpha, \ write \ P(X=4)` in terms of `alpha` .

Explanation

`P(X=1)=P(X=2)=a `

`P(X=4)=? `

`P(x=r)=\ ^{n} C_{r} p^{r} q^{n-r} `

`P(x=1)=\ ^{n} C_{1} p^{1} q^{n-1} `

`=n times p times q^{n-1}(1) `

`P(x=2)=\ ^{n} C_{2} p^{2} q^{n-2} `

`=frac{n(n-1)}{2} times p^{2} q^{n-2}(2)`

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