1. Using Venn Diagrams A and B are events in a sample space S such that P(A) 0.7. P(B) P(A and B) 0.2. 0.4. and (a) Draw a Venn diagram showing the overlapping sets A and B and fill in the probabilities of the four regions formed. (b) Find the probability that A occurs but B does not. (e) Find the probability that neither A nor B occurs. (d) Find the probability that A or B occurs. (e) Are events A and B independent? (That is, does P(A|B) = P(A)?)