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 8 be the analogous event for a MasterCard where P(A) = 0.45, P(8) = 0.45, and P{A n 8) = 0.20. Calculate and interpret each of the following probabilities (a Venn diagram might help). (Round your answers to four decimal places.) P(B | A) P(B' I A) P(A | B) P(A' | B) Given that the selected individual has at least one card, what is the probability that he or she has a Visa Card?

Explanation / Answer

Let C be the event that the student has atleast one card.

P(C) = P(A) + P(B) - P(A B) = 0.45 +0.45 -0.20 = 0.70

So the probability that person possess atleast one card is 0.70.

Now out of that, the probability that he has a visa card is = 0.45 / 0.70 ..... (Conditional Probability)

Required probability = 0.45/0.70 = 0.6428

Note: The venn diagram would also give you the same result.

Hope this helps. Please rate ASAP. Thanks. :D :D

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