Suppose that Dave can decide to go to work by one of three modes of transportation, car, bus, or commuter train. Because of high traffic, if he decides to go by car, there is a 50% chance he will be late. If he goes by bus, which has special reserved lanes but is sometimes overcrowded, the probability of being late is only 20%. The commuter train is almost never late, with a probability of only 5%, but is more expensive than the bus. Suppose that Dave is late one day, and his boss wishes to estimate the probability that he drove to work that day by car. Since he does not know which mode of transportation Dave usually uses, he gives a prior probability of 1/3 to each of the three possibilities. What is the boss' estimate of the probability that Dave drove to work? Suppose that a coworker of Dave's knows that he almost always takes the commuter train to work, never takes the bus, but sometimes, 10% of the time takes the car. What is the co-workers probability that Art drove to work that day, given that he was late?