Question: A man takes either a bus or the subway to work with probabilities .3 and .7, respectively. When he takes the bus, he is late

A man takes either a bus or the subway to work with probabilities .3 and .7, respectively. When he takes the bus, he is late 30% of the days. When he takes the subway, he is late 20% of the days. If the man is late for work on a particular day, what is the probability that he took the bus?

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