Question

Choose the correct option from the given alternatives:

For a binomial distribution, n = 5. If P(X = 4) = P(X = 3), then p = ______

Options

• `1/3`

• `3/4`

• 1

• `2/3`

Answer 1

`2/3`

Explanation:

P(X = 4) = P(X = 3)

∴ `""^5C_4  p^4  q = "^5C_3  p^3  q^2`

∴ 5p = 10q

∴ 5p = 10(1 - p)

∴ p = `(10(1 - "p"))/5`

∴ p = 2 - 2p

∴ p + 2p = 2

∴ 3p = 2

∴ p = `2/3`