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

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