Question

Consider randomly selecting a student at a large university. Let A be the event that the selected student has a Visa card, let B be the analogous event for MasterCard, and let C be the event that the selected student has an American Express card. Suppose that P(A) = 0.6, P(B) = 0.4, and P(ANB) = 0.3, suppose that PC) = 0.2, P(ANC) = 0.13, PB N C) = 0.1, and P(ANBNC) = 0.07. (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 and a MasterCard but not an American Express card? (c) Calculate P( BA) and P( AB). P( BA) = P( AB) = Interpret P(BA) and P( A B). (Select all that apply.) OP( AB) is the probability that a student does not have a MasterCard or a Visa card. P(B A) is the probability that a student does not have a MasterCard or a Visa card. P( A B) is the probability that given that a student has a MasterCard, they also have a Visa card. O P( A B) is the probability that given that a student has a Visa card, they also have a MasterCard. OP ( B A) is the probability that given that a student has a Visa card, they also have a MasterCard. OP ( B A) is the probability that given that a student has a MasterCard, they also have 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 probability that she or he has at least one of the other two types of cards?

Answer 1

O We want, PLAUBUC) EP) +PCB) +PCC) -PCAQB) - CANO -P(BOS) + P CAOBAO) = 0.6+ 0.4 to 2 - 0.3 -0.13 -0.01 +0.07 = 0.74 ans PCB1A) = POBOA C Bayes thettes) PCA) to =P CANB) PCA) = 0:3 A 0.6 PCA1B) = CAOB PCB) 0.3 0.75 Ans 0.5 Ans

P(A|B) is the probability of occurrence of A given B has occurred. So it is the probability of owning a visa card given he already has a MasterCard. So option c is correct.

Similarly P(B|A) is the probability of owning a MasterCard given he already has a visa card. So option e is correct.

d) We want, P(A$\cap$B|C) = P(A$\cap$B$\cap$C)/P(C) = 0.07/0.2 = 0.35