Question

John is traveling to Washington DC for work and can either fly down to DC, take the train, or drive to get to his business meeting. If he flies into DC, he is delayed 40% of the time. If he takes the train into DC, he is delayed 30% of the time. If he drives, he is delayed 20% of the time. John flied 60% of the time, takes the train 30% of the time, and drives 10% of the time.

Given that John is delayed, what is the probability that he flew?

Answer 1

let A: Event that John travel by air B: 1 train o drive E: e is delayed Given (E/A)=40%-0.4, PLE/B) = 30%=0.3 Pl Ele) = 20%20:2, PLA)=60% 20.6 P(B)- 30% : 03, PIC): 10“), = 0.1 DAI. PLANE) (A) = P PLANE) P(E) PIADE) + P(BNE) + P(CNE) PIEZA) PIA) PC) PL A)+ PLE/B) PCB) +P(E7) PCC) 0.4 0.6 0.4x0.6+ 0.3x0.3+0+2x001 - 35 = 0.6857