Question

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

Options

• `9/13`

• `2/13`

• `4/13`

• `11/13`

Answer 1

In a binomial distribution, n = 4 and 2P(X = 3) = 3P(X = 2), then q = `underlinebb(4/13)`.

Explanation:

Given, n = 4

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

`\implies` 2. ⁴C₃ p³q = 3 ⁴C₂p²q²

`\implies (2 . 4!)/(3!1!)p = (3 . 4!)/(2!2!)q`

`\implies` p = `9/4 q`

∵ p + q = 1

`\implies 9/4 q + q` = 1

`\implies (13q)/4` = 1

`\implies` q = `4/13`