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) = 0.45, P(B) = 0.35, and P(A B) = 0.20. Calculate and interpret each of the following probabilities (a Venn diagram might help). (Round your answers to four decimal places.) Cannot figure out the trick to questions with the compliments.

(a) P(B | A) .4444 .

(b) P(B' | A)

(c) P(A | B) .5714

(d) P(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

(b) P(B' | A) = P(B' and A)/P(A)

In terms of venn diagram P(B' and A) this will be those areas of A which are not B. In other words This will be the area of A - the common area of A and B.

P(B' | A) = P(B' and A)/P(A) = (0.45 - 0.20)/0.45 = 0.5556

(d) P(A' | B) = P(A' and B)/P(B) = (0.35 - 0.20)/0.35 = 0.4286

(e) P(A | (A or B)) = 0.45/(0.45+0.35 - 0.20) = 0.75

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