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John finds a bill on his desk. He has three options: ignore it and leave it on his own desk, move the bill over to his wife Mary's desk, or pay the bill immediately. The probability that he leaves it on his own desk is 0.7. The probability that he moves it to Mary's desk is 0.2. The probability that he pays the bill immediately is 0.1. Similarly, if Mary finds a bill on her desk she can choose to leave it on her own desk, put it on John's desk, or pay it immediately. The probability that it remains on her desk is 0.4. The probability she moves it to John's desk is 0.3. The probability she pay: it immediately is 0.3. Once a bill is paid it will not return to either of the desks. Assume this is a Markov Chain process. Set up the transition matrix and use it to answer the following questions. (Give your answers correct to three decimal places.) (a) Find the probability a bill now on John's desk will be paid within two days. (b) What is the probability a bill now on John's desk will be on Mary's desk 3 days later? (c) On average, how many days will pass before a bill placed on John's desk is paid? days

John finds a bill on his desk. He has three options: ignore it and leave it on his own desk, move the bill over to his wife Mary's desk, or pay the bill immediately. The probability that he leaves it on his own desk is 0.7. The probability that he moves it to Mary's desk is 0.2. The probability that he pays the bill immediately is 0.1. Similarly, if Mary finds a bill on her desk she can choose to leave it on her own desk, put it on John's desk, or pay it immediately. The probability that it remains on her desk is 0.4. The probability she moves it to John's desk is 0.3. The probability she pay: it immediately is 0.3. Once a bill is paid it will not return to either of the desks. Assume this is a Markov Chain process. Set up the transition matrix and use it to answer the following questions. (Give your answers correct to three decimal places.) (a) Find the probability a bill now on John's desk will be paid within two days. (b) What is the probability a bill now on John's desk will be on Mary's desk 3 days later? (c) On average, how many days will pass before a bill placed on John's desk is paid? days

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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John finds a bill on his desk. He has three options: ignore it and leave it on his own desk, move the bill over to his wife Mary's desk, or pay the bill immediately. The probability that he leaves it on his own desk is 0.7. The probability that he moves it to Mary's desk is 0.2. The probability that he pays the bill immediately is 0.1. Similarly, if Mary finds a bill on her desk she can choose to leave it on her own desk, put it on John's desk, or pay it immediately. The probability that it remains on her desk is 0.4. The probability she moves it to John's desk is 0.3. The probability she pays it immediately is 0.3. Once a bill is paid it will not return to either of the desks. Assume this is a Markov Chain process. Set up the transition matrix and use it to answer the following questions. (Give your answers correct to three decimal places.) (a) Find the probability a bill now on John's desk will be paid within two days. (b) What is the probability a bill now on John's desk will be on Mary's desk 3 days later? (c) On average, how many days will pass before a bill placed on John's desk is paid? days
Transcribed Image Text:John finds a bill on his desk. He has three options: ignore it and leave it on his own desk, move the bill over to his wife Mary's desk, or pay the bill immediately. The probability that he leaves it on his own desk is 0.7. The probability that he moves it to Mary's desk is 0.2. The probability that he pays the bill immediately is 0.1. Similarly, if Mary finds a bill on her desk she can choose to leave it on her own desk, put it on John's desk, or pay it immediately. The probability that it remains on her desk is 0.4. The probability she moves it to John's desk is 0.3. The probability she pays it immediately is 0.3. Once a bill is paid it will not return to either of the desks. Assume this is a Markov Chain process. Set up the transition matrix and use it to answer the following questions. (Give your answers correct to three decimal places.) (a) Find the probability a bill now on John's desk will be paid within two days. (b) What is the probability a bill now on John's desk will be on Mary's desk 3 days later? (c) On average, how many days will pass before a bill placed on John's desk is paid? days
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