Q81 / 150 · MHT CET 2023 (11 May Shift 1) · Mathematics

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

  • Correct answer
    A
    $\frac{1}{4}$
  • B
    $\frac{1}{2}$
  • C
    $\frac{1}{8}$
  • D
    $\frac{1}{5}$

Solution

$\begin{aligned} & \text { 9. } p(X=4)=p(X=2) \text { and } n=6 \\ & \Rightarrow 9 \times{ }^6 C_4 p^4 q^2={ }^6 C_2 p^2 q^4 \\ & \Rightarrow 9 p^2=q^2 \\ & \Rightarrow 3 p=q \\ & \Rightarrow 3 p=1-p \\ & \Rightarrow p=\frac{1}{4}\end{aligned}$

Hence, the correct answer is option: 'A'.

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