An experiment succeeds twice as often as it fails. The probability of at least 5 successes in the six trials of this experiment is

Step-by-step solution

Let p be the probability of successes and q be the probability of failure. p = 2 q and p + q = 1 gives p = 2 3 and q = 1 3 For having at least 5 successes in 6 trials, Required probability = C 5 6 2 3 5 1 3 + C 6 6 2 3 6 = C 1 6 2 3 5 1 3 + C 0 6 2 3 6 = 6.2 5 + 64 3 6 = 256 729