Question

There are 5 radar stations and the probability of a single radar station detecting an enemy plane is 0.55. What is the probability that the number of stations that detect a plane is no more than 3? Round your answer to nearest hundredth

Answer 1

This is a binomial distribution with n = 5, p = 0.55, q = 1 - 0.55 = 0.45, x = 0, 1, 2, 3

P(x) = nCx p^x q^(n - x)
P(x ≤ 3) = 1 - P(x > 3) = 1 - [P(4) + P(5)]
P(4) = 5C4 x (0.55)^4 x (0.45) = 0.2059
P(5) = 5C5 x (0.55)^5 x 1 = 0.0503

P(x ≤ 3) = 1 - (0.2059 + 0.0503) = 1 - 0.2562 = 0.7438