MHT CET · Maths · Probability
For a Binomial distribution, \(n=6\), if \(9 P(X=4)=P(X=2)\), then \(q=\)
- A \(\frac{1}{2}\)
- B \(\frac{1}{4}\)
- C \(\frac{3}{4}\)
- D \(\frac{2}{5}\)
Answer & Solution
Correct Answer
(C) \(\frac{3}{4}\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & 9 P(X=4)=P(X=2) \\ & \Rightarrow 9{ }^n C_4 P^4 \cdot q^{n-4}={ }^n C_2 P^2 q^{n-2} \\ & \Rightarrow 9 \frac{{ }^n C_4}{{ }^n C_2}=\frac{q^2}{P^2}=\left(\frac{q}{1-q}\right)^2 \\ & \Rightarrow \frac{q}{1-q}=3 \Rightarrow q=\frac{3}{4}\end{aligned}\)
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