If the difference between the mean and variance of a binomial variate is 5 9 , then the probability of getting 2 successes for an event when the experiment is conducted 5 times, is

Step-by-step solution

Mean =n p , variance =n p q aligned & n p-n p q= 5 9 & 5(p-p q)= 5 9 =p(1-q)= 1 9 & since, p+q=1, p=1-q & p^2= 1 q p= 1 3 , q=1- 1 3 = 2 3 aligned So probability of getting 2 successes = ^5 C ₂ ( 1 3 )^2 ( 2 3 )^3=10 1 9 8 27 = 80 243