Question: Let A, B, C be events such that A (B C) = (complete sample space). It is known that P(A B C) = 0.1, P(B

Let A, B, C be events such that A (B C) = (complete sample space).

It is known that P(A B C) = 0.1, P(B C) = 0.2, P(C) = 0.4,

A and C are independent conditional on B, and A and B are independent conditional on C.

(a) Calculate P(A B) and P(A C).

(b) Calculate P(A) and P(B).

(c) Calculate P(B | A C) and P(B|A). Are B and C independent conditional on A?

(d) Identify two dependent events among A, B and C.

(e) Are A, B and C independent?

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