In a Binomial distribution, $n=4$ and $2 P(X=3)=3 P(X=2)$, then $q=$

In a Binomial distribution, $n=4$ and $2 P(X=3)=3 P(X=2)$, then $q=$
  1. $\frac{2}{13}$
  2. $\frac{11}{13}$
  3. $\frac{9}{13}$
  4. $\frac{4}{13}$

Solution

$\begin{aligned} & 2 P(x=3)=3 p(x=2) \\ & \Rightarrow 2 \times{ }^4 c_3(1-q)^3 q=3 \times{ }^4 c_2(1-q)^2 q^2 \\ & \Rightarrow 2 \times 4 \times(1-q)=3 \times 6 \times q \\ & \Rightarrow \frac{4}{9}=\frac{q}{1-q} \\ & \Rightarrow q=\frac{4}{13}\end{aligned}$

Asked in: MHT CET 2022 (08 Aug Shift 1)

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