Question: On rainy days, Joe is late to work with probability .3; on nonrainy days, he is late with probability .1. With probability .7, it will

On rainy days, Joe is late to work with probability .3; on nonrainy days, he is late with probability .1. With probability .7, it will rain tomorrow.
(a) Find the probability that Joe is early tomorrow.
(b) Given that Joe was early, what is the conditional probability that it rained?

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