Question

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)

Answer 1

The answer is D.

Explanation:

Answer 2

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.