Question

If random variable `x ∼ b (n = 5, P = 1/3)`, then P(2 < X < 4) is equal to ______.

Options

• `80/243`

• `40/243`

• `40/343`

• `80/343`

Answer 1

If random variable `x ∼ b (n = 5, P = 1/3)`, then P(2 < X < 4) is equal to `underlinebb(40/243)`.

Explanation:

Since, X ∼ B = `(n = 5, p = 1/3)`

∵ p + q = 1

`\implies 1/3 + q` = 1

`\implies` q = `2/3`

∴ p(2 < X < 4) = p(X = 3)

= `""^5C_3 (1/3)^3 (2/3)^2`

= `10 xx 4/3^5`

= `40/243`