Problem Set 4

Assigned: Oct. 20
Due: Oct. 27.

Let A, B, and C be events. You are given that

Prob(A) = 0.6.
Prob(B | A) = 0.8.
Prob(B | ~A) = 0.3. ("~A" means "not A")
Prob(C | A) = 0.9.
Prob(C | ~A) = 0.2
You are also given that B and C are conditionally independent given A; and that B and C are conditionally independent given ~A.

Compute the following values: