Bob can decide to go to work either by car, bus, or commuter train. If he decides to go by car, there is a 50% chance he will be late due to traffic. 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, there is a 1% chance that he is late, but is more expensive than the bus. What is the probability that Bob drove to work today given he arrives late to work?
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