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Prove that if Pr B A then it follows

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.

(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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