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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(A n B) = 0.3, suppose that P(C) = 0.2, P(A n C) = 0.14, P(Bn C) = 0.1, and P(A n Bn C) = 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(B | A) and P(A | B). P(B | A) = P(A|B) = Interpret P(B | A) and P(A | B). (Select all that apply.) P(A|B) is the probability that given that a student has a MasterCard, they also have a Visa card. P(B | A) is the probability that given that a student has a MasterCard, they also have 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 Visa card, they also have a MasterCard. P(A|B) is the probability that a student does not have a MasterCard or a Visa card. P(B | A) is the probability that given that a student has a Visa card, they also have a MasterCard. (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?

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(A n B) = 0.3, suppose that P(C) = 0.2, P(A n C) = 0.14, P(Bn C) = 0.1, and P(A n Bn C) = 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(B | A) and P(A | B). P(B | A) = P(A|B) = Interpret P(B | A) and P(A | B). (Select all that apply.) P(A|B) is the probability that given that a student has a MasterCard, they also have a Visa card. P(B | A) is the probability that given that a student has a MasterCard, they also have 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 Visa card, they also have a MasterCard. P(A|B) is the probability that a student does not have a MasterCard or a Visa card. P(B | A) is the probability that given that a student has a Visa card, they also have a MasterCard. (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?

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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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(A n B) = 0.3, suppose that P(C) = 0.2, P(A n C) = 0.14, P(Bn C) = 0.1, and P(A n Bn C) = 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(B | A) and P(A | B). P(B | A) = P(A|B) = Interpret P(B | A) and P(A | B). (Select all that apply.) P(A|B) is the probability that given that a student has a MasterCard, they also have a Visa card. P(B | A) is the probability that given that a student has a MasterCard, they also have 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 Visa card, they also have a MasterCard. P(A|B) is the probability that a student does not have a MasterCard or a Visa card. P(B | A) is the probability that given that a student has a Visa card, they also have a MasterCard. (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?
Transcribed Image Text: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(A n B) = 0.3, suppose that P(C) = 0.2, P(A n C) = 0.14, P(Bn C) = 0.1, and P(A n Bn C) = 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(B | A) and P(A | B). P(B | A) = P(A|B) = Interpret P(B | A) and P(A | B). (Select all that apply.) P(A|B) is the probability that given that a student has a MasterCard, they also have a Visa card. P(B | A) is the probability that given that a student has a MasterCard, they also have 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 Visa card, they also have a MasterCard. P(A|B) is the probability that a student does not have a MasterCard or a Visa card. P(B | A) is the probability that given that a student has a Visa card, they also have a MasterCard. (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?
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