Question: Prove that if Pr (B | A), then it follows that (a) Pr (A, B) = Pr (A) Pr (B) and (b) Pr (A, B)

Prove that if Pr (B | A), then it follows that
(a) Pr (A, B) = Pr (A) Pr (B) and
(b) Pr (A, B) = Pr (A).
Furthermore, show that if, then the two conditions above do not hold as well.

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