Which statement implies that A and B are independent events? A. P(B|A) = P(B A) B. P(B|A) = P(B) P(A) C. P(B|A) = P(A) D. P(B|A) = P(B)

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asked Sep 14, 2019 160k views

2 Answers

Riiwo · Answer 1 · 2019-09-20T17:53:22+0000

The events
A,B are independent if and only if
$P(A\cap B)=P(A)\cdot P(B)$ . Under this condition, we have conditional probabilities

$P(A\mid B)=(P(A\cap B))/(P(B))=(P(A)\cdot P(B))/(P(B))=P(A)$

$P(B\mid A)=P(B)$

so the answer is D.