Professor Stan der Deviation can take one of two routes onhis way home from work. On the

Chapter 2, Problem 88

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Professor Stan der Deviation can take one of two routes onhis way home from work. On the first route, there are fourrailroad crossings. The probability that he will be stoppedby a train at any particular one of the crossings is .1, andtrains operate independently at the four crossings. The otherroute is longer but there are only two crossings, independentof one another, with the same stoppage probability foreach as on the first route. On a particular day, ProfessorDeviation has a meeting scheduled at home for a certaintime. Whichever route he takes, he calculates that he will belate if he is stopped by trains at at least half the crossingsencountered.a. Which route should he take to minimize the probabilityof 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-crossingroute?