You live on Keswick Ridge and commute to campus. Suppose that you have the option of crossing the river at the dam, the Westmoreland St Bridge, or the Princess Margaret Bridge. You tend to take the dam about half the time, and otherwise are equally likely to take one of the other two bridges. Your probability of lateness is 0.16, 0.10, and 0.19 for the three bridges respectively.
(a) If you choose a bridge at random, what is the probability that you will be late?
(b) If you drive to the city and choose one of the two city bridges (PM or WS) at random, what is the probability that you will be late?
(c) If you are late, what is the probability that you chose to cross at the dam?