Let X be the number of successes in ‘n’ independent Bernoulli trials with probability of success p = 3 4 . The least value of ‘n’ so that P X ≥ 1 ≥ 0.9375 is….

Step-by-step solution

We have, p = 3 4 , q = 1 - p = 1 4 It is given that P X ≥ 1 ≥ 0.9375 = 1 - P X = 0 ≥ 0.9375 = 1 - n C 0 p 0 g n - 0 ≥ 0.9375 = 1 - 1 4 n ≥ 0.9375 = 1 - 0.9375 ≥ 1 4 n = 0.0625 ≥ 1 4 n = 625 10000 ≥ 1 4 n = 1 16 ≥ 1 4 n = 16 ≤ 4 n ⇒ n = 2