If $X \sim B(4, p)$ and $2 P(X=3)=3 P(X=2)$ then value of $p$ is

If $X \sim B(4, p)$ and $2 P(X=3)=3 P(X=2)$ then value of $p$ is
  1. $\frac{9}{13}$
  2. $\frac{4}{13}$
  3. $\frac{1}{13}$
  4. $\frac{12}{13}$

Solution

Given $X \sim B(4, p)$ and $2 P(X=3)=3 P(X=2)$ $2\left[{ }^{4} C_{3} p^{3} q^{1}\right]=3\left[{ }^{4} C_{2} p^{2} q^{2}\right]$ $2 \times 4 p^{3} q=3 \times 6 p^{2} q^{2}$ $\therefore p=\frac{9 q}{4} \Rightarrow p=\frac{9}{4}(1-p) \Rightarrow p=\frac{9}{4}-\frac{9}{4} p$ $\left(1+\frac{9}{4}\right) p=\frac{9}{4} \Rightarrow \frac{13 p}{4}=\frac{9}{4} \Rightarrow p=\frac{9}{13}$

Asked in: MHT CET 2020 (14 Oct Shift 2)

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