Chapter 6.4, Problem 30E

Two different airlines have a flight from Los Angeles to New York that departs each weekday morning at a certain time. Suppose that E denotes the event that the first airline’s flight is fully booked on a particular day, and F denotes the event that the second airline’s flight is fully booked on that same day.

Suppose that P(E) = 0.7, P(F) = 0.6, and P(E ∩ F) = 0.54.

1. a. Calculate P(E|F）， the probability that the first airline’s flight is fully booked given that the second airline’s flight is fully booked. (Hint: See Example 6.12.)
2. b. Calculate P(F|E).