An airline estimates that 97% of people booked on their flights actually show up.If the airline books 71 people on a flight for which the maximum number is 69,what is the probability that the number of people who show up will exceed the capacity of the plane?

A) 0.6324
B) 0.3676
C) 0.6410
D) 0.1150
E) 0.2526

This problem can be solved using the binomial probability formula, but given the choices and the nature of the question, a simpler approach is to consider the complement. The probability that the number of people showing up does not exceed the capacity is the sum of the probabilities of exactly 69 or fewer people showing up. Since calculating this directly for each case (0 to 69) would be cumbersome, we consider the complement, which is the probability of more than 69 people showing up (i.e., 70 or 71 people showing up, given that 97% of people booked show up). The complement approach simplifies the calculation, and the given answer choice B (0.3676) aligns with the probability of the event's complement, which is the probability that the flight will be overbooked. This is a simplified explanation; the exact calculation involves more detailed binomial probability or normal approximation methods.