The probability of success for the Binomial distribution satisfying the relation, $4 P(X=4)=P(X=2)$ and…
The probability of success for the Binomial distribution satisfying the relation, $4 P(X=4)=P(X=2)$ and having the parameter $n=6$, is
- $\frac{1}{5}$
- $\frac{5}{6}$
- $\frac{1}{6}$
- $\frac{1}{3}$
Solution
$\begin{aligned} & 4 \cdot P(x=4)=P(x=2) \\ & \Rightarrow 4 \cdot{ }^6 C_4 P^4 \cdot q^2={ }^6 C_2 p^2 q^4 \\ & \Rightarrow \frac{p^2}{q^2}=\frac{1}{4}\end{aligned}$
$\begin{aligned} & \Rightarrow 3 p=1 \\ & \Rightarrow p=\frac{1}{3}\end{aligned}$
Asked in: MHT CET 2022 (10 Aug Shift 2)
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