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.)

Question

Mathematics

Phillip Colon

8 October, 23:37

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.)

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Answers (1)

Know the Answer?

Haley Morris · Answer 1

A) P (E | F) = 0.817

B) P (F | E) = 0.613

Step-by-step 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.