A binomial random variable $\mathrm{X}$ satisfies 9.p $(\mathrm{X}=4)=\mathrm{p}(\mathrm{X}=2)$ when…
A binomial random variable $\mathrm{X}$ satisfies 9.p $(\mathrm{X}=4)=\mathrm{p}(\mathrm{X}=2)$ when $\mathrm{n}=6$. Then $\mathrm{p}$ is equal to
- $\frac{1}{4}$
- $\frac{1}{2}$
- $\frac{1}{8}$
- $\frac{1}{5}$
Solution
$\begin{aligned} & \text { 9. } p(X=4)=p(X=2) \text { and } n=6 \\ & \Rightarrow 9 \times{ }^6 C_4 p^4 q^2={ }^6 C_2 p^2 q^4 \\ & \Rightarrow 9 p^2=q^2 \\ & \Rightarrow 3 p=q \\ & \Rightarrow 3 p=1-p \\ & \Rightarrow p=\frac{1}{4}\end{aligned}$
Asked in: MHT CET 2023 (11 May Shift 1)
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