Juan goes to college each day by any one of car or bus or walking. The probability that he goes by car is $$\(0.2\)$$, the probability that he goes by bus is $$\(0.45\)$$ and the probability that he walks is $$\(0.35\)$$. When Juan goes by car, the probability that he arrives early is $$\(0.6\)$$. When he goes by bus, the probability that he arrives early is $$\(0.1\)$$. When he walks he always arrives early. Find the probability that Juan goes to college by car given that he arrives early. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................

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