In a binomial distribution B ( n , p ) , the sum and product of the mean & variance are 5 and 6 respectively, then find 6 ( n + p - q ) is equal to :-

Step-by-step solution

For the binomial distribution B ( n ,   p ) , Mean = n p and Variance = n p q Sum of mean and variance = n p + n p q = 5 ⇒ n p ( 1 + q ) = 5 ⇒ n 2 p 2 ( 1 + q ) 2 = 25 ....(1) Product of mean and variance = n p . n p q = 6 ⇒ n 2 p 2 q = 6 ....(2) Put the value of n 2 p 2 from equation (2) into equation (1): 6 q ( 1 + q ) 2 = 25 ⇒ 6 q 2 + 12 q + 6 = 25 q ⇒ 6 q 2 - 13 q + 6 = 0 ⇒ ( 3 q - 2 ) ( 2 q - 3 ) = 0 ⇒ q = 2 3 ,   3 2 where q = 2 3 accepted ∴   p =