If events X and Y are independent, what must be true? Check all that apply.

All these are true when X and Y are independent events:

1) The occurrence or lack of event X does not influence the occurrence of event Y, and the occurrence or lack of event Y does not influence the occurrence of event X.

2) P (X∩Y) = P (X) * P (Y)

3) P (X | Y) = P (X) ... this is the probability of X given Y is equal to the probability of X.

4) P (Y | X) = P (Y)

5) P (A∪B) = P (A) + P (B) - P (A∩B)