Consider randomly selecting a student at a large university. LetA be the event that the selected student has a Visa card,let B be the analogous event for MasterCard, and letC be the event that the selected student has an AmericanExpress 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) = 0.12,P(B ∩ C) = 0.1, and P(A∩ B ∩ C) = 0.08.
a)What is the probability that the selected student has at leastone of the three types of cards?
b)What is the probability that the selected student has both aVisa 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)If we learn that the selected student has an American Expresscard, what is the probability that she or he also has both a Visacard 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 theother two types of cards?
