Two different airlines have a flight from Los Angeles to New York that departs each weekday morning at a certain time. Let E denote the event that the first airline’s flight is fully booked on a particular day, and let F denote the event that the second airline’s flight is fully booked on that same day. Suppose that P(E) = .7, P(F ) = .6, and P(E ∩ F ) = .54.
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.
b. Calculate P(F | E) .
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