MHT CET · Maths · Probability
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
- A \(\frac{1}{4}\)
- B \(\frac{1}{2}\)
- C \(\frac{1}{8}\)
- D \(\frac{1}{5}\)
Answer & Solution
Correct Answer
(A) \(\frac{1}{4}\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \text { 9. } p(X=4)=p(X=2) \text { and } n=6 \\ & \Rightarrow 9 \times{ }^6 C_4 p^4 q^2={ }^6 C_2 p^2 q^4 \\ & \Rightarrow 9 p^2=q^2 \\ & \Rightarrow 3 p=q \\ & \Rightarrow 3 p=1-p \\ & \Rightarrow p=\frac{1}{4}\end{aligned}\)
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