An experiment succeeds twice as often as it fails. Then the probability, that in the next 6 trials there will be atleast 4 successes, is

Step-by-step solution

Experiment succeeds twice as often as it fails. According to the given condition, if ' p ' is success and ' q ' is failure, then p=2 q aligned p + q =1 & 2 q + q =1 & q = 1 3 and p = 2 3 aligned Here, n =6 Let X be the random variable X B ( n , p ) Required probability aligned & = P ( X 4) & = P ( X =4)+ P ( X =5)+ P ( X =6) & = ^6 C ₄ p ^4 q ^2+ ^6 C ₅ p ^5 q + ^6 C ₆ p ^6 & =15 ( 2 3 )^4 ( 1 3 )^2+6 ( 2 3 )^5 ( 1 3 )+ ( 2 3 )^6 & = 496 729 aligned