Brian arrives to the College Ave student center bus stop at 5:00 PM. The waiting time for the bus to Busch campus is a random va
riable that satisfies roughly the exponential distribution (see below). If there is a traffic congestion on route 18, the average waiting time for the bus is 25 minutes. If there is no traffic congestion, the average waiting time is 7 minutes. Ordinarily there is a 35% chance of traffic congestion on route 18 around that time of the day. Brian waited 20 minutes until the bus showed up. What is the probability that there is traffic congestion? Carefully pose the question in terms of conditional probability, explain how you find the solution, and then use R to calculate it. Search R to learn how to conduct calculations regarding the exponential distribution.
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