(4) During the peak of the holiday season, if you are trying to travel from Akro

Question

(4) During the peak of the holiday season, if you are trying to travel from Akron to Miami, you can go through either Atlanta or Chicago or Washington DC 50% of the flights out of Akron go to Chicago, 30% go to Atlanta and the rest of them to Washington. Due to the holiday rush, your chances of getting a seat at all on a flight from Chicago to Miami is 20%, that for Atlanta to Miami is 10% and that for Washington DC to Miami is 10%. If you were ultimately able to fly from Akron to Miami, what are the (conditional) chances that you went through Atlanta? T21

Explanation / Answer

Let C shows the event that flight go to Chicago, A shows the event that flight go to Allanta and W shows the event that flight goes to Washington. So

P(C) = 0.50, P(A) = 0.30, P(W) = 1 -0.50 -0.30 =0.20

Let M shows the event that fligh tgoes to Miami so

P(M|C) = 0.20, P(M|A) =0.10, P(M|W) = 0.10

By the Baye's theorem the required probability is

P(A|M) = [P(M|A)P(A) ] / [P(M|A)P(A) + P(M|C)P(C) + P(M|W)P(W) ] = [0.10*0.30] / [ 0.10*0.30 + 0.20*0.50 + 0.10*0.20 ] = 0.03 / [0.03 + 0.10 + 0.02] = 0.20

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