Return to the credit card scenario of Exercise 12 (Section 2.2), and let C be the event that the selected student has an American Express card. In addition to P(A) = .6, P(B) = .4, and P(A n B) = .3, suppose that P(C) = .2, P(A n C) = .15, P(B n C) = .1, and P(A n B n C) = .08.

A. What is the probability that the selected student has at least one of the three types of cards?

B. What is the probability that the selected student has both a Visa card and a MasterCard but not an American Express card?

C. Calculate and interpret P(B | A) and also P(A | B).

D. If we learn that the selected student has an American Express card, what is the probability that she or he also has both a Visa card and a MasterCard?

E. Given that the selected student has an American Express card, what is the probability that she or he has at least one of the other two types of cards?