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) = 0.8, P(F) = 0.6, and P(E Two different airlines have a flight from Los Ange F) = 0.49.(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

A) P(E | F) = 0.817

B) P(F | E) = 0.613

Explanation:

From the question,

P(E) = 0.8, P(F) = 0.6

P(E∩F) = 0.49

A) From conditional probability;

P(E | F) = [P(E∩F)]/P(F) = 0.49/0.6 = 0.8167 which is approximately 0.817 in 3 decimal places.

B) Also, P(F | E) = [P(F∩E)]/P(E) = 0.49/0.8 = 0.6125 which is approximately 0.613 in 3 decimal places.