Question

Which statement implies that A and B are independent events?

And the answers are:
P(B|A) = P(B A)

P(B|A) = P(B)
P(A)

P(B|A) = P(A)
P(B|A) = P(B)

Answer 1

The kast one is the answer. It is the only one unaffected by A to any degree.

Answer 2

The correct option is D.

Explanation:

Two events are known as independent events if the probability of one event does not affect the probability of second event.

If A and B are two independent event, then

`P(A\cap B)=P(A)\cdot P(B)` .... (1)

The formula of conditional probability is

`P(B|A)=(P(A\cap B))/(P(A))`

If A and B are two independent event, then by using equation (1) we get

`P(B|A)=(P(A)\cdot P(B))/(P(A))`

`P(B|A)=P(B)`

Therefore the correct option is D.