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If $X$ follows a binomial distribution with parameters $n = 6$ and $4 (P (X = 4)) = P (X = 2)$ then $p =$

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$1 / 2$

$1 / 4$

$1 / 6$

$1 / 3$

answer is D.

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Detailed Solution

We have,

$\begin{array}{l} 4 P (X = 4) = P (X = 2) \\ \Rightarrow 4^{6} C_{4} p^{4} q^{2} =^{6} C_{2} p^{2} q^{4} \\ \Rightarrow 4 p^{2} = q^{2} \\ \Rightarrow 4 p^{2} = (1 - p)^{2} \Rightarrow 3 p^{2} + 2 p - 1 = 0 \Rightarrow p = \frac{1}{3} \end{array}$

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