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The prior probabilities for events A and B are P(A)= 0.80 and P(B)= 0.20. It is also known that P(A B) = 0. Suppose P(CA)

The prior probabilities for events A and B are P(A)= 0.80 and P(B)= 0.20. It is also known that P(A B) = 0. Suppose P(CA) = 0.10 and P (CB) = 0.20.

1. Are A and B mutually exclusive? Why or why not?

2. Compute P(A C) and P(B C)

3. Compute P(C)

4. Apply for Bayes' theorem to compute P(AC) and P(BC)

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