A random variable X B(n, p) follows a binomial distribution with n = 6 . If 9P(X = 4) = P(X = 2) , then the probability of success p is..

Step-by-step solution

Given X B(n, p) with n = 6 . The probability mass function is P(X = k) = ^ n C_ k p^k (1-p)^ n-k . Substituting k = 4 and k = 2 in the given condition 9P(X = 4) = P(X = 2) : 9 ⁶C₄ p^4 (1-p)^2 = ⁶C₂ p^2 (1-p)^4 Since ⁶C₄ = ⁶C₂ = 15 , dividing both sides by 15 p^2 (1-p)^2 gives: 9p^2 = (1-p)^2 Taking the square root on both sides, since p > 0 and 1-p > 0 : 3p = 1 - p 4p = 1 p = 0.25 Answer: 0.25