The probability of a bomb hitting a bridge is 2 3 . Two direct hits are needed to destroy the bridge. The minimum number of bombs required such that the probability of bridge being destroyed is greater than 3 4 , is

Step-by-step solution

Let the number of bombs required = n Probability of a bomb hitting the target is 2 3 ∴ Probability of atleast 2 hits = 1 − 1 3 n − C n 1 2 3 1 1 3 n − 1 > 3 4 ⇒ 2 n + 1 3 1 3 n - 1 < 1 4 ⇒ 4 3 2 n + 1 < 3 n - 1 ⇒ n ≥ 4