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 h own desk is 0.6. The probability that he moves it to Mary's desk is 0.3. 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 0.2. The probability she moves it to John's desk is 0.5. The probability she pays it immediately is 0.3. Once a bill is paid it will not return to either of the desks. In other words, there is a 0% chance that a bill will return to John's desk or Mary's desk once it goes to the mailbox. Assume this is a Markov Chain process. Set up the transition matrix and use it to answer the following questions. (Hint: When determining what your matrix labels should be, think of the location of the bill, not the action done to it. For example, the label "moves to the other desk" would not be a valid label.) (a) What is the probability that a bill currently on John's desk will be paid within two days? .19 (b) What is the probability that a bill currently on John's desk will be on Mary's desk 3 days later? 156
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 h own desk is 0.6. The probability that he moves it to Mary's desk is 0.3. 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 0.2. The probability she moves it to John's desk is 0.5. The probability she pays it immediately is 0.3. Once a bill is paid it will not return to either of the desks. In other words, there is a 0% chance that a bill will return to John's desk or Mary's desk once it goes to the mailbox. Assume this is a Markov Chain process. Set up the transition matrix and use it to answer the following questions. (Hint: When determining what your matrix labels should be, think of the location of the bill, not the action done to it. For example, the label "moves to the other desk" would not be a valid label.) (a) What is the probability that a bill currently on John's desk will be paid within two days? .19 (b) What is the probability that a bill currently on John's desk will be on Mary's desk 3 days later? 156
Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter11: Data Analysis And Probability
Section11.8: Probabilities Of Disjoint And Overlapping Events
Problem 2C
Related questions
Concept explainers
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
Topic Video
Question
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 4 steps
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, probability and related others by exploring similar questions and additional content below.Recommended textbooks for you
Holt Mcdougal Larson Pre-algebra: Student Edition…
Algebra
ISBN:
9780547587776
Author:
HOLT MCDOUGAL
Publisher:
HOLT MCDOUGAL
Holt Mcdougal Larson Pre-algebra: Student Edition…
Algebra
ISBN:
9780547587776
Author:
HOLT MCDOUGAL
Publisher:
HOLT MCDOUGAL