Question

If A and B are two independent random variables, is P(A|B)<P(A)?

Answer 1

For independent variables `A` and `B` `P(A//B)=P(A)`

Explanation:

If variables `A` and `B` are independent, then

`P(AnnB)=P(A)*P(B)`.

According to definition of `P(A//B)`

`P(A//B)=(P(AnnB))/(P(B))`.

So:

`P(A//B)=(P(A)*P(B))/(P(B))`

So finally `P(A//B)=P(A)`