Professor Stan der Deviation can take one of two routes on his way home from work. On the rst route, there are four railroad crossings. The proba- bility that he will be stopped by a train at any par- ticular one of the crossings is .1, and trains operate independently at the four crossings. The other routeis longer but there are only two crossings, indepen- dent of one another, with the same stoppage proba- bility for each as on the rst route. On a particular day, Professor Deviation has a meeting scheduled at home for a certain time. Whichever route he takes, he calculates that he will be late if he is stopped by trains at at least half the crossings encountered.
a. Which route should he take to minimize the probability of being late to the meeting?
b. If he tosses a fair coin to decide on a route and he is late, what is the probability that he took the four-crossing route?