Question

In a binomial distribution, n = 4 and 2P(X = 3) = 3P(X = 2), then q = ______.

विकल्प

• ${\displaystyle \frac{9}{13}}$

• ${\displaystyle \frac{2}{13}}$

• ${\displaystyle \frac{4}{13}}$

• ${\displaystyle \frac{11}{13}}$

Answer 1

In a binomial distribution, n = 4 and 2P(X = 3) = 3P(X = 2), then q = ${\displaystyle \underline{\frac{4}{13}}}$.

Explanation:

Given, n = 4

and 2P(X = 3) = 3P(X = 2)

${\displaystyle \Rightarrow }$ 2. ⁴C₃ p³q = 3 ⁴C₂p²q²

${\displaystyle \Rightarrow \frac{2.4!}{3!1!}p=\frac{3.4!}{2!2!}q}$

${\displaystyle \Rightarrow }$ p = ${\displaystyle \frac{9}{4}q}$

∵ p + q = 1

${\displaystyle \Rightarrow \frac{9}{4}q+q}$ = 1

${\displaystyle \Rightarrow \frac{13q}{4}}$ = 1

${\displaystyle \Rightarrow }$ q = ${\displaystyle \frac{4}{13}}$