A group of customers at a local library borrowed books from the library for two weeks then returned them. When they returned them, they checked out a new book. Of the people that returned a fiction book, 10% of them checked out a history book, 20% of them checked out a self-help book, and the rest checked out another fiction book. Of the ones that returned a history book, 30% of them checked out a book on fiction and 70% checked out another history book. Of those that returned a self-help book, 10% checked out a history book, 60% checked out a fiction book, and the rest checked out another self-help book. 17. Draw a fully labeled transition state diagram and write the transition matrix. Be sure you designate which rows and columns corresponded to the type of book.18. If there were an equal number of readers of each of the three book types, what would be the distribution of book types after one transition?19. If everyone had a fiction book to start with, what is the probability that someone has a self-help book after two transitions? ## Library Book Transition ExerciseA group of customers at a local library borrowed books for two weeks and then returned them. Upon returning, they checked out a new book. The distribution of book checkouts is as follows:- **Fiction Books:** - 10% of these customers checked out a history book. - 20% checked out a self-help book. - The remaining checked out another fiction book.- **History Books:** - 30% of these customers checked out a fiction book. - 70% checked out another history book.- **Self-Help Books:** - 10% checked out a history book. - 60% checked out a fiction book. - The rest checked out another self-help book.### Questions17. **Draw a fully labeled transition state diagram and write the transition matrix.** - Ensure you indicate which rows and columns correspond to the type of book.18. **If there were an equal number of readers of each of the three book types,** - What would be the distribution of book types after one transition?19. **If everyone started with a fiction book,** - What is the probability that someone will have a self-help book after two transitions?

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Description: A group of customers at a local library borrowed books from the library for two weeks then returned them. When they returned them, they checked out a new book. Of the people that returned a fiction book, 10% of them checked out a history book, 20% of

(17). Draw a fully labelled transition state diagram and write transition matrix: In the given…

Answered: A group of customers at a local library…

A First Course in Probability (10th Edition)

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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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A group of customers at a local library borrowed books from the library for two weeks then returned them. When they returned them, they checked out a new book. Of the people that returned a fiction book, 10% of them checked out a history book, 20% of them checked out a self-help book, and the rest checked out another fiction book. Of the ones that returned a history book, 30% of them checked out a book on fiction and 70% checked out another history book. Of those that returned a self-help book, 10% checked out a history book, 60% checked out a fiction book, and the rest checked out another self-help book.

17. Draw a fully labeled transition state diagram and write the transition matrix. Be sure you designate which rows and columns corresponded to the type of book.

18. If there were an equal number of readers of each of the three book types, what would be the distribution of book types after one transition?

19. If everyone had a fiction book to start with, what is the probability that someone has a self-help book after two transitions?

## Library Book Transition Exercise

A group of customers at a local library borrowed books for two weeks and then returned them. Upon returning, they checked out a new book. The distribution of book checkouts is as follows:

- **Fiction Books:**
- 10% of these customers checked out a history book.
- 20% checked out a self-help book.
- The remaining checked out another fiction book.

- **History Books:**
- 30% of these customers checked out a fiction book.
- 70% checked out another history book.

- **Self-Help Books:**
- 10% checked out a history book.
- 60% checked out a fiction book.
- The rest checked out another self-help book.

### Questions

17. **Draw a fully labeled transition state diagram and write the transition matrix.**
- Ensure you indicate which rows and columns correspond to the type of book.

18. **If there were an equal number of readers of each of the three book types,**
- What would be the distribution of book types after one transition?

19. **If everyone started with a fiction book,**
- What is the probability that someone will have a self-help book after two transitions?

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