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On rainy days, Tim is late to school with probability 0.4; on snowy days, he is...

On rainy days, Tim is late to school with probability 0.4; on snowy days, he is late with probability 0.7; otherwise, he is late with probability 0.2. Suppose that tomorrow will rain with probability 0.5, and will snow with probability 0.2.

(a) Find the probability that Tim is late tomorrow.

(b) Given that Tim was early, what is the conditional probability that it rained.

Math   Statistics-And-Probability   
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