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Consider randomly selecting a student at a large university. Let A be the event that the...

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Basic Math

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?

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