Traffic signals were installed at an intersection involving two one-way streets. Suppose 85% of the vehicles will decelerate when they see the amber light, whereas 10% will accelerate and 5% are "indecisive" and simply continue with the same speed. Five percent of those who accelerated will eventually run a red light, and only 2% of indecisive drivers will be forced to run a red light. All of those who decelerated are able to stop before the red light.

a. For a vehicle encountering the amber light at this intersection, what is the probability that it will run the red light?

b. If a vehicle were found to have run a red light, what is the probability that the driver had accelerated?

c. The likelihood of an accident resulting from a vehicle running the red light (referred to as a problem vehicle) is studied as follows. Suppose 60% of the time, vehicles are waiting on the other street as the start of their green light cycle, ready to cross the intersection. Most of these driver, say 80%, are cautious before they entered the intersection, whereas the rest are not cautious. Given the presence of a problem vehicle in the intersection zone, a cautious driver can avoid the problem 95% of the time, whereas 20% of the noncautious drivers will collide with the problem vehicle. What is the probability that a problem vehicle will lead to an accident?

d. Suppose the annual traffic flow in one of these one-way streets is 100,000 vehicles and 5% of them would encounter the amber signal light. Estimate the number of accidents per year in the intersection that would be traced back to vehicles running through a red light on that street.