Answer to Question #6390 in Statistics and Probability for Melissa

Question #6390
A commuter can take any one of two routes on his way home from work. On the ¯rst route, there are four railroad crossings. The probability that he will be stopped by a train at any particular one of the crossings is .1, and trains operate independently at the four crossings. The other route is longer, but there are only two crossing, independent of one another, with the same stoppage probability for each as on the ¯rst route. On a particular day, the commuter 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?
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