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) = nCx Px (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,
⇒ 5C2p2q5-2 = 95C3p3q5-3
⇒ 10p2q3 = 9×10p3q2
⇒ 10q = 90p {As , p≠0 and q ≠ 0}
⇒ q = 9p
⇒ 1-p = 9p ⇒ 10p = 1
∴ p = 1/10
