Consider randomly selecting a student at a certain university, and let A denote

Question

Consider randomly selecting a student at a certain university, and let A denote the event that the selected individual has a Visa credit card and B be the analogous event for a MasterCard where P(A) = 0.50, P(B) = 0.45, and P(A n B) = 0.20. Calculate and interpret each of the following probabilities (a Venn diagram might help). (Round your answers to four decimal places.) (a)-P(81A) B' A) (c) PAIB) A' B) (e) Given that the selected individual has at least one card, what is the probability that he or she has a Visa Card?

Explanation / Answer

a)

P(B|A) =P(A nB) /(A) =0.20/0.5 =0.40

b) P(B'|A )=1-P(B|A) =1-0.40 =0.60

c) P(A|B) =P(A n B)/P(B) =0.2/0.45 =0.4444

d) P(A'|B) =1-P(A|B) =1-0.4444 =0.5556

e)

P(Visa card given at least one card) =P(A|AUB) =P(A)/(P(A)+P(B)-P(A n B)) =0.5/(0.5+0.45-0.20)

=0.5/0.75=0.6667

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