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Title: Consider randomly selecting a student at a certain university, and let A denote the event that the ... Post by: ogyno84 on Oct 17, 2012 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. Suppose that P(A) = 0.1, P(B) = 0.6, and P(A ? B) = 0.05.
calculate the probability of this event? thanks in advance Title: Consider randomly selecting a student at a certain university, and let A denote the event that the ... Post by: bio_man on May 28, 2017 Similar 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. Suppose that P(A) = 0.5; P(B) = 0.4; and P(A N B) = 0.25. (A N B) = The intersection of A and B. a) If the randomly selected student has a Visa card, what is the probability they have a MasterCard? b) Calculate and interpret P(B'|A). c) Calculate and interpret P(A|B) d) If the randomly selected student has a MasterCard, what is the probability they do not have a Visa card? e) Given that the selected individual has at least one card, what is the probability that he or she has a Visa card? Answer: a) P(MasterCard|Visa) = P(Visa and MasterCard)/P(Visa) = P(B|A) = P(A n B)/P(A) = .25/.5 = 1/2 = .5 b) P(B'|A) = P(no Master Card|Visa) or the probability of no MasterCard given a Visa = P(no Master Card and Visa)/P(Visa) = P(B' n A)/P(A) P((B'UB) n A) = P(A) Therefore, P(B'A) + P(BA) = P(A) P(B'A) = P(A) - P(BA) = .5 - .25 = .25 Therefore, P(B'|A) = P(B' n A)/P(A) = .25/.5 = 1/2 = .5 c) P(A|B) = P(Visa|MasterCard) =the probability of a Visa given a MasterCard = P(Visa and MasterCard)/P(MasterCard) = .25/.4 = 5/5 = .625 d) P(no Visa|MasterCard) = P(A'|B) = P(A'B)/P(B) P(A'B) + P(AB) = P(B) Therefore, P(A'B) = P(B) - P(AB) = .4 - .25 = .15 P(A'B)/P(B) = .15/.4 = 3/8 = .375 e) P(Visa Card|Visa Card or MasterCard) = P(Visa Card and (Visa Card or MasterCard))/P(Visa Card or MasterCard) = P(Visa Card)/P(Visa Card or MasterCard) (if A is a subset of B, A n B = A, and clearly having a Visa Card is a subset of having a Visa Card or MasterCard) P(Visa Card or MasterCard) = P(Visa Card) + P(MasterCard) - P(Visa Card or MasterCard) = .4 + .5 - .25 = .65 Then, P(Visa Card)/P(Visa Card or MasterCard) = .5/.65 = 10/13 ≈ 0.769230769230769 |