Question

PLEASE HELP!!!

Explain the difference between P(A|B) and P(A)and P(B) given that events A and B are independent events.

Answer 1

for independent A and B, P(A|B) = P(A)

Explanation:

The definition of conditional probability is ...

P(A|B) = P(A&B)/P(B)

When A and B are independent, ...

P(A&B) = P(A)·P(B)

so the conditional probability is ...

P(A|B) = (P(A)·P(B))/P(B) = P(A) . . . . . for independent A and B

In words, when A and B are independent, the probability of A given B is the same as the probability of A. That is, the probability of B has no effect on the probability of A.