Two different airlines have a flight from Los Angeles to New

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) = 0.7, P(F) = 0.6, andP(E F) = 0.56.

(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. (Round your answer to three decimal places.)


(b) Calculate P(F | E). (Round your answer to three decimal places.)

Solution

a)
P(E | F) = P( E n F) / P(F) = 0.56 / 0.6 = 0.933

b)
P(F | E) = P( F n E) / P(E) = 0.56/0.7 = 0.8