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. Suppose that P(A) = 0.4, P(B) = 0.5, and P(A ? B) = 0.35. (a) Compute the probability that the selected individual has at least one of the two types of cards (i.e., the probability of the event A union B). Correct: Your answer is correct. (b) What is the probability that the selected individual has neither type of card? Correct: Your answer is correct. (c) Describe, in terms of A and B, the event that the selected student has a Visa card but not a MasterCard. A' ? B' A' ? B A ? B' A' union B' A union B' Correct: Your answer is correct. Calculate the probability of this event. Incorrect: Your answer is incorrect.

Explanation / Answer

easy p(A) = .4 p(B) = .5 p(A n B ) = .35 a ) p ( A u B ) = p(a)+p (B)-p(A n B) = .4+.5-.35 = .55 b) neither type of card = 1-p(A)-p(B) = 1-.4-.5 = .1 C) only visa but not master = P(A )-P(A n B) = .4-.35 = .05

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