Question 1 Express each of the following events in terms of the events A, B and C as well as the operations of complement, union and intersection, and draw the corresponding Venn diagrams: (a) at least one of the events A, B, C occurs; (b) at most one of the events A, B, C occurs; (c) none of the events A, B, C occurs; (d) all three events A, B, C occur; (e) exactly one of the events A, B, C occurs. Question 2 Events A and B satisfy the following probability statements: P(A) = 2/3, P(B) = 1/4 and P(AU B) = 4/5. Find P(An B), P(An B*) and P(An B). Question 3 Events A and B satisfy the following probability statements: P(A) = 0.25 and P(B) = 0.1. Find the smallest and largest possible values for P(A U B). Question 4 Events A and B satisfy the following probability statements: P(A) = 0.9 and P(B) = 0.8. Find the smallest and largest possible values for P(An B). Question 5 Let A, B, C be three sets. Show that P(AU BUC) = P(A) + P(B) + P(C) - P(AnB) - P(AnC) - P(BnC) + P(AnBnC)