Question

If r.v. X ∼ B`(n = 6, p = 1/4)`, then P(3 < X < 5) = ______ 

Options

• `135/4096`

• `135/4906`

• `153/4096`

• `153/4906`

Answer 1

If r.v. X ∼ B`(n = 6, p = 1/4)`, then P(3 < X < 5) = `underline(135/4096)`.

Explanation:

Here, n = 6, p = `1/4`

and q = `1 - 1/4 = 3/4`

∴ P(3 < X < 5) = P(X = 4)

= `""^6"C"_4(1/4)^4(3/4)^2`

= `135/4096`