1. Consider randomly selecting a student at a large university, and let A be the
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Question
1. Consider randomly selecting a student at a large university, and let A be the event that the selected student has a Visa card, B be the analogous event for MasterCard, and C be the event that the selected student has an American Express card. Suppose that P(A)- .6, P(B).4, P(C)- .2, P(An B)- .3, P(A n C)-. 15, P(B n C)-. 1, and P(A n B n C)-.08 a. What is the probability that the selected student has at least one of the three types of cards? b. What is the probability that the selected student has both a Visa card anda MasterCard but not an American Express card? c. Calculate and interpret P(BIA) d. Calculate and interpret P(AlB) e. If we learn that the selected student has an American Express card, what is the probability that she or he also has both a Visa card and a MasterCard? f. Given that the selected student has an American Express card, what is the probability that she or he has at least one of the other two types of cards?Explanation / Answer
SolA:
P(AUBUC)=P(A)+P(B)+P(C)-P(Aand B)-P(B and C)-P(A and C)-P(A and B and C)
=0.6+0.4+0.2-0.3-0.1-0.15-0.08
=0.57
the probability that the selected student has atleast one of the three types of cards is
0.57
Solutionc:
P(B/A)=P(A and B)/P(A)
=0.3/0.6
=0.5
probability that a student has master card given that he already has visa card=0.5
Solutiond:
P(A/B)=P(A and B)/P(B)
=0.3/0.4
=0.75
probability that a student has visa card given that he already has American card=0.75
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