Question

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, and P(E ∩ F) = 0.54.
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. (Round your answer to three decimal places.)
b. Calculate P(F | E). (Round your answer to three decimal places.)

Answer 1

Answer:

A) P(E|F) = 0.900

B) P(F|E) = 0.771

Step-by-step explanation:

P(E) = 0.7

P(F) = 0.6

P(E n F) = 0.54

A) P(E|F), the probability that the first airline's flight is fully booked given that the second airline's flight is fully booked is given mathematically as

P(E|F) = P(E n F)/P(F) = 0.54/0.6 = 0.900

B) P(F|E), the probability that the second airline's flight is fully booked given that the first airline's flight is fully booked is given mathematically as

P(F|E) = P(E n F)/P(E) = 0.54/0.7 = 0.771