Question: 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

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 ⋂ B) = .3, suppose that P(C) = .2, P(A ⋂ C) = .15, P(B ⋂ C) = .1, and P(A ⋂ B ⋂ 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?

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