Consider randomly selecting a student at a large university. Let A be the event that the selected student has a Visa card, let B be the analogous event for MasterCard, and let C be the event that the selected student has an American Express card. Suppose that P(A) = 0.6, P(B) = 0.4, and P(A n B) = 0.3, suppose that P(C) = 0.2, P(A n C) = 0.14, P(Bn C) = 0.1, and P(A n Bn C) = 0.07. (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 P(B | A) and P(A | B). P(B | A) = P(A|B) = Interpret P(B | A) and P(A | B). (Select all that apply.) P(A|B) is the probability that given that a student has a MasterCard, they also have a Visa card. P(B | A) is the probability that given that a student has a MasterCard, they also have a Visa card. P(B | A) is the probability that a student does not have a MasterCard or a Visa card. P(A|B) is the probability that given that a student has a Visa card, they also have a MasterCard. P(A|B) is the probability that a student does not have a MasterCard or a Visa card. P(B | A) is the probability that given that a student has a Visa card, they also have a MasterCard. (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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