Question

If X follows binomial distribution with parameters n = 5, p and P(X = 2) = 9, P(X = 3), then p = ______.

Answer 1

If X follows binomial distribution with parameters n = 5, p and P(X = 2) = 9, P(X = 3), then p = `1/10`.

Explanation:

Given that: P(X = 2) = 9P(X = 3)

⇒ `""^5"C"_2 "p"^2 "q"^3` = 9. `""^5"C"_3 "p"^3 "q"^2`

⇒ `1/9 = (""^5"C"_3 "p"^2 "q"^2)/(""^5"C"_2 "p"^2 "q"^3)`

⇒ `1/9 = "p"/"q"`  .......`[because ""^5"C"_3 = ""^5"C"_2]`

⇒ 9p = q

⇒ 9p = 1 – p

⇒ 9p + p = 1

⇒ 10p = 1

∴ p = `1/10`