In February, a major airline had 77.5% of their flights arrive on time. Assume that the event that a given flight arrives on time is independent of the event that another flight arrives on time. a. A writer plans to take four separate flights for her publisher next month. Assuming the airline has the same on-time performance as in February, what is the probability that all four flights arrive on time? b. Discuss how realistic it is to assume that the on-time arrivals of the different flights are independent.

The probability that the flight of the airline arrives on time is .775. The problem tells us that the events are independent and asks us what is the probability that 4 flights arrive on time.

Since the probability is independent we can simply multiply the probabilities of each flight arriving on time.

Probability that all 4 flights arrive on time = (.775)(.775)(.775)(.775) = 0.3607.

b) How realistic it is to assume that the on-time arrivals are independent?

This assumption is not very realistic, considering that if one flight is not on time, it will obviously affect all the other flights since the planes are constantly connected to each other and if the flights are using one same plane, the fact that this plane is not on-time will affect the next flight.