Complete ALL the questions correctly to get the full credit 1. Consider a random

Question

Complete ALL the questions correctly to get the full credit 1. Consider a randomly selecting student at a certain university, and let A denotes the event that the selected individual has a Visa credit card and B be the analogous event for MasterCard. Suppose that PA-05 , P(B)=04, and P(A n B) = 0.25. [40 points] Compute the probability that the selected individual has at least one of the two types of cards. a. b. What is the probability that the selected individual has neither type of cards? If two students are selected randomly, what is the probability that both of them do not have visa cards? c. Given that a student has a Visa card, what is the probability that student has a Mater card as well? d.

Explanation / Answer

P(A) = 0.5

P(B) = 0.4

P(A B) = 0.25

a) P(A U B) = P(A) + P(B) - P(A B)

                    = 0.5 + 0.4 - 0.25

                    = 0.65

b) P((A U B)') = 1 - P(A U B) = 1 - 0.65 = 0.35

c) P(A') = 1 - P(A) = 1 - 0.5 = 0.5

P(both not having Visa cards) = P(A') * P(A') = 0.5 * 0.5 = 0.25

d) P(B | A) = P(B A) / P(A) = 0.25 / 0.5 = 0.5

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