1. You are driving on Kapiolani Boulevard toward Waikiki one weeknight. Without any warning, you find yourself in a bumper-to-bumper traffic jam. In your mind, you come up with three possible scenarios to explain the traffic: there is either heavy construction (C), a special event (E), or a major accident (A). You weren't aware of there being any scheduled construction, but then again you didn't check before leaving home; so, you think Pr(C) is 1/5. You also didn't hear of any special event being held in Waikiki tonight, but there is always some parade, protest, or block party going on; so you think Pr(E) is 11/20. That leaves Pr(A) at 1/4. You are assuming that these three possibilities are mutually exclusive.

Before you know it, the traffic has turned out to be so bad that you haven't moved an inch in 30 minutes. Based on your past experience, it is pretty rare for road construction to result in such standstill traffic (T) - just 1/5 of the time there is road construction does traffic get this bad. If a special event were scheduled, you think there would be a 2/5 chance of traffic being this bad -road closures can back up traffic a lot, but at least there should be some police around to keep things moving. Assuming there were a major accident, you think there is a 4/5 chance of this kind of heavy traffic occurring - there could be damaged vehicles blocking lanes, emergency personnel, rubber-necking, etc.

a) Draw a tree diagram representing the different possibilities and their probabilities. (2 pts.)

b) What is the probability that there is a major accident given that there is heavy traffic? (3 pts.)

Pr(A|T) =