, a student goes to school by bus

Question

, a student goes to school by bus on Monday and Tuesday, by train on Wednesday, and by light bus on Thursday and Friday. The probabilities that the student is late to school if he travels by bus, train and light bus are 0.15, 0.35 and 0.1, respectively. Given that the student is late to school on one day, what is the probability that the day is Wednesday? Assume that the student does not go to school on Saturday and Sunday.

Answer 1

The key to a lot of problems of this type is interpreting the conditional probability elements. What is being asked here is the probability that a late day is Wednesday, given that the student is late on some day of the week.

If we let W be the event of being Wednesday and L be the event of being late on some day of the week, then P(W | L) = P(W ∩ L) / P(L). The probability of being late, or P(L), on some day of the week is the sum of all the probabilities of being late on Monday through Friday, which is 0.15 + 0.15 + 0.35 + 0.1 + 0.1 = 0.85. The probability of being late and it being Wednesday, or P(W ∩ L), is 0.35. So P(W | L) = 0.35/0.85 ≈ 0.4118.