Question

An experiment succeeds thrice as often as it fails. Find the probability that in the next five trials, there will be at least 3 successes.

Answer 1

An experiment succeeds thrice as often as it fails.

⇒ p = P(getting success) = and

q = P(getting ***) = Here, number of trials = n = 5

By binomial distribution, we have

P(X = x) = nCxqn - xpx, x = 0, 1, 2, ....n

P(X = r) = 5Cr(3/4)r(1/4)5 - r

Now , P(getting at least 3 success) = P(X = 3) + P(X = 4) + P(X = 5)

= 5C3(3/4)3(1/4)2 + 5C4(3/4)4(1/4)1 + 5C5(3/4)5

= (3/4)3[10 x 1/16 + 15 x 1/16 + 9 x 1/16] = 27/64 x 34/16 = 459/512