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 ? B) = 0.3, suppose that P(C) = 0.2, P(A ? C) = 0.11, P(B ? C) = 0.1, and P(A ? B ? 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) =

(d) Interpret P(B | A) and P(A | B). (Select all that apply.)

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.

P(A | B) is the probability that given that a student has a Visa card, they also have a MasterCard.

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 MasterCard, they also have a Visa card.

(e) 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?

(f) 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?