Question

randomly selecting a student at a large university. Let A be the event that the selected student has a Visa card, let 8 be the s event for MasterCard, and let C be the event that the selected student has an American Express card. Suppose that Pe n C)-0.1, and P(A n BnC)-0.08 A)-0.6,代8)-04, and (a) What is the probability that the select ed 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 and a MasterCard but not an American Express card? (c) Calculate P(B | A) and P(A I B) P(BIA) Interpret A) and FA I B). (Select all that apply.) D PA | B) Is the probability that given that a student has a MasterCard, they also have a Visa card P(B I A) is the probability that given that a student has a MasterCard, they also have a Visa card. p(A β) is the probability that a student does not have a MasterCard or a Visa card. PA I B) is the probability that given that a student has a Visa card, they also have a MasterCard. D P(B I A) is the probability that given that a student has a Visa card, they also have a MasterCard P(B I A) Is the probability that a student does not have a MasterCard or a Visa card. (d) 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? e) Given that the selected student has an American Express card, what is the probablity that she or he has at least one of the other two tyl of ar&indows

Answer 1

a)

at least one =P(AUBUC)=

P(A)+P(B)+P(C )-P(AnB)-P(BnC)-P(AnC)+P(AnBnC)

=

0.76

b)

P(A n B n C')=P(A n B)-P(A n B n C)=0.3-0.08 =0.22

c)

P(B|A)=P(A n B)/P(B)=0.3/0.6 =0.5

P(A|B)=P(A n B)/P(B)=0.3/0.4 =0.75

P(A|B) is the probability that given that a student has a Master card ; they also has a Visa card

P(B|A) is the probability that given that a student has a Visa card ; they also has a master card

d)

P(A n B|C)=P(A n B nC)/P(C)=0.08/0.2 =0.4

e)

P(A u B|C) =P((A u B ) n C))/P(C)=(0.1+0.12-0.08)/0.2=0.7