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It is given that the discrete random variable is $X ~ B (n, p)$ and $P (X = 2) = P (x = 3) .$

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2-p

3-p

p-2

p-3

answer is B.

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Detailed Solution

$\begin{array}{l} P (x = 2) = P (x = 3) \\ n C_{2} P^{2} q^{n - 2} = n C_{3} P^{3} q^{n - 3} \\ \Rightarrow \frac{1}{n - 2} = \frac{P}{3 q} \Rightarrow 3 q = p (n - 2) \\ \Rightarrow n p = 3 - P \end{array}$

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