Fill in the blanks in the following question:

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

p = 1/10

As n = 5 {representing no. of trials}

p = probability of success

As it is a binomial distribution.

∴ probability of failure = q = 1 – p

Given,

P(X = 2) = 9.P(X = 3)

The binomial distribution formula is:

P(x) = _nC_x P^x (1 – P)^{n – x}

Where:

x = total number of “successes.”

P = probability of success on an individual trial

n = number of trials

Using binomial distribution,

⇒ ⁵C₂p²q^5-2 = 9⁵C₃p³q^5-3

⇒ 10p²q³ = 9×10p³q²

⇒ 10q = 90p {As , p≠0 and q ≠ 0}

⇒ q = 9p

⇒ 1-p = 9p ⇒ 10p = 1

∴ p = 1/10