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) = 0.50, P(B) = 0.45, and P(A B) = 0.30.Calculate and interpret each of the following probabilities (a Venn diagram might help). (Round your answers to four decimal places.)

(a)    P(B | A)


(b)    P(B' | A)


(c)    P(A | B)


(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

A)P(B | A) = P(A INTERSECTION B) / P(A)

= 0.30/0.50 = 3/5

B)  P(B' | A) = P( A INTERSECTION B') / P(A) = 0.50/0.50 = 1

C) P(A | B) = P( A INTERSECTION B)/ P(B)

= 0.30/0.45 = 0.66

D)P(A'/B) = P(A' INTERSECTION B)/P(B) = 0.45/0.45 =1

E)HERE IS THE ANSWER WILL BE DIRECT AS VISA PROBABILITY = 0.50

AND NON MASTER CARD PROBABILITY = 1 -0.45 = 0.55

HENCE ANSWER = 0.50/0.55 = 0.90

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