A certain person goes for a run each morning. When he leaves the house for his run, he is equally likely to go out either the front or the back door and similarly when he returns, he is equally likely to go to either the front or the back door. The runner owns 3 pairs of running shoes which he takes off after the run at whichever door he happens to be. If there are no shoes at the door from which he leaves to go running, he runs barefoot. We are interested in determining the proportion of time that he runs barefoot. 1. Set this problem up as a discrete time Markov chain. Give the states and the one-step transition probability matrix. 2. Determine the proportion of days that he runs barefoot.

A certain person goes for a run each morning. When he leaves the house for his run, he is equally likely to go out either the front or the back door and similarly when he returns, he is equally likely to go to either the front or the back door. The runner owns 3 pairs of running shoes which he takes off after the run at whichever door he happens to be. If there are no shoes at the door from which he leaves to go running, he runs barefoot. We are interested in determining the proportion of time that he runs barefoot. 1. Set this problem up as a discrete time Markov chain. Give the states and the one-step transition probability matrix. 2. Determine the proportion of days that he runs barefoot.

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...

See similar textbooks

Similar questions

Each of the questions in this boxpertains to rollinga pair of fair dice. Find the probability that the sum is less than 5 and the sum is prime.
The player pays a fee of $5 to play. The player then rolls a 12-sided die three times. If the player rolls a 7 on any of the three rolls, they win a prize. The prize is determined by the number of 7s rolled. If the player rolls one 7, they win $5. If the player rolls two 7s, they win a $10. If the player rolls three 7s, they win $20. Give evidence that the player will theoretically win 20-40% of the time
Please show your solution. If a pair of dice is rolled, what is the probability of getting a a.) sum of 10? b.) sum of 9? c.) sum of at least 8? d.) sum of at most 6?
In a certain university the probability of randomly selecting a student that studies mathematics is 0.6 while the probability of randomly selecting a student studying literature is 0.45. Which of the following statements CAN NEVER BE TRUE? I. The probability of selecting a student studying mathematics given that he studies literature is 0. II. The probability of selecting a student that studies both science and mathematics is 0.27. O Both Statements I and Il. O StatementI only. O Neither Statement I not I. O Statement II only.
The response already posted ons ite is not being accepted..Looking for a different outcome. Reeba randomly picks one of her 3 children to help her clean the house. She randomly assigns the child she picks to either clean the kitchen, living room or bedroom. Label her children O (Oldest), M (Middle) or Y (Youngest) and the job K (Kitchen), L (Living room) or B (Bedroom). [Use the order in which these are listed, abbreviate with captial letters, separate with commas, no spaces]
Four salesmen play "odd man out" to see who pays for lunch. They each flip a coin, and if there is a salesman whose coin doesn't match the others he pays for lunch. To clarify, the "odd man" must get heads while the other three get tails OR he must get tails while the other three get heads. Of course, since it is possible for two men get heads and two men get tails, not all flips will result in finding an "odd man". If this occurs the salesmen would be forced to flip again. What is the probability that there is an "odd man" the first time they flip?
In a drawing organized at the office, Monique purchased 10 of the100 tickets sold. If there are four prizes to be won, what is theprobability that she will win at least one prize?
A father and his three children decide to hold a vote to select an after dinner activity. They will either see a play or a movie. If the majority of the family agrees on a preferred activity, then they will do that activity. If two family members vote to see a play and the other two family members vote to watch a movie, then (since the father will pay for the activity), the father's vote will be used to break the tie. (a) How many winning coalitions are there in this situation? (b) Find one of the children's Banzhaf power index.
Read the paper above and answer question # 4 only
If the student attends class on a certain Friday, then he is five times as likely to be absent the next Friday as to attend. If the student is absent on a certain Friday, then he is three times as likely to attend class the next Friday as to be absent again.
Two players play a game with the following rules: Player 1 puts on a blindfold while player two throws a die. The number that he gets is put aside as the "Target value". Then player two throws another die three times while giving player 1 information on weather he gets a lesser number than the target, equal to the target or greater than the target. Imagine that you are player one and you are handed the information that player two got [Lesser, equal, greater]. Deduce the probabilities of each possible target given the information.