Solution. Let the probability of a route B bus be P(B) and the probability of a bus being late be P(L)

Let the probability of a route B bus be P(B) and the probability of a bus being late be P(L).

Since there are only two bus routes the probability of a route A bus is P(B’).

Bayes’ theorem states .

We are given that

NOTE! This question could have been done using a tree diagram and conditional probability.

“At least” problems

We have already met the idea of the total probability being one and that sometimes it is easier to find a probability by subtracting the answer from one. In some situations we do not have a choice in this, as shown in the example below.