Let in a Binomial distribution, consisting of 5 independent trials, probabilities of exactly 1 and 2 successes be 0.4096 and 0.2048 respectively. Then the probability of getting exactly 3 successes is equal to

Step-by-step solution

Let p be the probability of success. aligned & P ( X =1)=0.4096 and P ( X =2)=0.2048 & ^5 C ₁ p ^1 q ^4=0.4096 and ^5 C ₂ p ^2 q ^3=0.2048 & 5 pq ^4=0.4096 and 10 p ^2 q ^3=0.2048 & 10 p ^2 q ^3 5 pq ^4 = 0.2048 0.4096 aligned aligned & 2 p q = 1 2 & 4 p = q & 4 p =1- p & 5 p =1 & p = 1 5 aligned aligned & q=1- 1 5 = 4 5 & aligned P(X=3) & = ^5 C₃ p^3 q^2 & =10 ( 1 5 )^3 ( 4 5 )^2 & =10 1 125 16 25 = 32 625 aligned aligned