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) = 0.35, and P(A B) = 0.25. 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

Let V = the student has a Visa card, and M = the student has a MasterCard.
P(V)=0.50,P(M)=0.35,P(VM)=0.25

1. P(B | A)=P(M | V)

P(M |V)=P(MV)/P(V)=0.25/.5= 0.5

2.P(B' | A) = P(M' | V)

=1-P(B/A)

=1-0.5
   = 0.5

3.P(A | B) = P (A B) / P(B)
= 0.25/ 0.35
   = 0.7143

4.  P(A' | B) = 1-P(A/B)
=1-0.7143
=0.2857

Hope this will be helpful. Thanks and God Bless You:-)

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