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?
