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3. Modified Exercise 2.36 A restaurant offers three ways of paying the bill: cash, credit card, and mobile payment (e.g., Apple Pay, Google Wallet). At the end of the day there were 200 paid bills. Some of the bills were paid with a mix of cash, credit card, and mobile payment. There were 36 bills paid with cash, 82 bills paid with credit card, and 113 bills paid by mobile payment. There were 8 bills that used cash and credit card, 13 bills that used cash and mobile payment, and 15 bills that used credit card and mobile payment. Five of the bills were paid with all three methods. (a) If two distinct bills are chosen at random, what is the probability that at least one was paid using two or more methods? (b) Suppose that a bill chosen at random and was paid using two or more methods. What is the probability it was paid with all three methods? (c) If a bill is chosen at random, what is the probability that the bill was paid fully using only one of the methods? (d) Suppose that a bill chosen at random was paid fully using only one of the methods. What is the probability the bill was paid by mobile payment?

3. Modified Exercise 2.36 A restaurant offers three ways of paying the bill: cash, credit card, and mobile payment (e.g., Apple Pay, Google Wallet). At the end of the day there were 200 paid bills. Some of the bills were paid with a mix of cash, credit card, and mobile payment. There were 36 bills paid with cash, 82 bills paid with credit card, and 113 bills paid by mobile payment. There were 8 bills that used cash and credit card, 13 bills that used cash and mobile payment, and 15 bills that used credit card and mobile payment. Five of the bills were paid with all three methods. (a) If two distinct bills are chosen at random, what is the probability that at least one was paid using two or more methods? (b) Suppose that a bill chosen at random and was paid using two or more methods. What is the probability it was paid with all three methods? (c) If a bill is chosen at random, what is the probability that the bill was paid fully using only one of the methods? (d) Suppose that a bill chosen at random was paid fully using only one of the methods. What is the probability the bill was paid by mobile payment?

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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3. Modified Exercise 2.36 A restaurant offers three ways of paying the bill: cash, credit card, and mobile payment (e.g., Apple Pay, Google Wallet). At the end of the day there were 200 paid bills. Some of the bills were paid with a mix of cash, credit card, and mobile payment. There were 36 bills paid with cash, 82 bills paid with credit card, and 113 bills paid by mobile payment. There were 8 bills that used cash and credit card, 13 bills that used cash and mobile payment, and 15 bills that used credit card and mobile payment. Five of the bills were paid with all three methods. (a) If two distinct bills are chosen at random, what is the probability that at least one was paid using two or more methods? (b) Suppose that a bill chosen at random and was paid using two or more methods. What is the probability it was paid with all three methods? (c) If a bill is chosen at random, what is the probability that the bill was paid fully using only one of the methods? (d) Suppose that a bill chosen at random was paid fully using only one of the methods. What is the probability the bill was paid by mobile payment?
Transcribed Image Text:3. Modified Exercise 2.36 A restaurant offers three ways of paying the bill: cash, credit card, and mobile payment (e.g., Apple Pay, Google Wallet). At the end of the day there were 200 paid bills. Some of the bills were paid with a mix of cash, credit card, and mobile payment. There were 36 bills paid with cash, 82 bills paid with credit card, and 113 bills paid by mobile payment. There were 8 bills that used cash and credit card, 13 bills that used cash and mobile payment, and 15 bills that used credit card and mobile payment. Five of the bills were paid with all three methods. (a) If two distinct bills are chosen at random, what is the probability that at least one was paid using two or more methods? (b) Suppose that a bill chosen at random and was paid using two or more methods. What is the probability it was paid with all three methods? (c) If a bill is chosen at random, what is the probability that the bill was paid fully using only one of the methods? (d) Suppose that a bill chosen at random was paid fully using only one of the methods. What is the probability the bill was paid by mobile payment?
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