Question

If X follows a binomial distribution with parameters n = 10 and p. If 4P(X = 6) = P(X = 4), then p = ______ 

Options

• `1/2`

• `1/4`

• `1/6`

• `1/3`

Answer 1

If X follows a binomial distribution with parameters n = 10 and p. If 4P(X = 6) = P(X = 4), then p = `underline(1/3)`.

Explanation:

4P(X = 6) = P(X = 4) 

⇒ `4. ""^10"C"_6 "P"^6 "q"^4 = ""^10"C"_4 "P"^4 "q"^6`

⇒ 4p² = q²

⇒ 4p² = (1 - p)²

⇒ 3p² + 2p - 1 = 0

⇒ p = `1/3`