This is a binomial probability problem. We can represent the fact that each bomb has a 1/5 probability of hitting (Y = yes) the bridge and a 4/5 probability of not hitting the bridge (N = no) with a "probability vector":





Then the probabilities of hitting the bridge with 0, 1, ..., 5, or 6 of the bombs will be the coefficients of the expansion of





Use the binomial theorem to expand that expression and find the appropriate coefficients. Since the bridge will be destroyed if it is hit by 2, 3, 4, 5, or 6 bombs, you could solve the problem by calculating those 5 coefficients. But it is much faster to calculate the probability that the bridge is NOT destroyed by calculating the probabilities that the bridge is hit by either 0 or 1 bomb; then the probability that the bridge is destroyed is 1 minus that probability.




The probability that the bridge will be destroyed is