Bob and Doug play a lot of Ping-Pong, but Doug is a much better player, and wins 90% of their games.To make up for this, if Doug wins a game he will spot Bob five points in their next game. If Doug wins again he will spotBob ten points the next game, and if he still wins the next game he will spot him fifteen points, and continue to spot himfifteen points as long as he keeps winning. Whenever Bob wins a game he goes back to playing the next game with noadvantage.It turns out that with a five-point advantage Bob wins 40% of the time; he wins 50% of the time with a ten-point advantageand 60% of the time with a fifteen-point advantage.Model this situation as a Markov chain using the number of consecutive games won by Doug as the states. There shouldbe four states representing zero, one, two, and three or more consecutive games won by Doug. Find the transition matrixof this system, the steady-state vector for the system, and determine the proportion of games that Doug will win in the longrun under these conditions.0 0 0P=|0 0 00 0 0S = 00.Proportion of games won by Doug = 0

Answered: Image /qna-images/answer/04ab3114-4239-42ae-b325-ffefa44de686.jpg

Answered: Bob and Doug play a lot of Ping-Pong,…

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

Alphonse donates a fair amount of money to various charities each year. He wants to know that his money is actually going to do the charity work, though. Suppose that 90% of the charities that he donates to are probably reputable and 10% are probably not. Also, suppose that 80% of the money that goes to the real charities ends up actually being used for the charity work, while 20% goes to administrative costs. If he donates the same amount to each charity, then what percent probably goes to actual charity work? 72| % SUBMIT ANSWER O ASK FOR HELP TURN IT IN to search 344 111 80 Y U D H. V
An instructor gave students the option to purchase an interactive program that allows them to answer questions during class and receive credit for participating. Alternatively, students could work an extra problem during weekly homework assignments. The instructor randomly selected 10 students, then randomly divided them into two groups of five each. One group was provided the interactive tool, the other group was asked to work the extra problem. The instructor knew from prior experience that the interactive tool increases attendance. The table below contains the final exam scores for the 10 students (on a scale from 0 to 100). Interactive: 65 78 84 88 96 Extra problem: 56 61 70 75 82 The instructor wishes to test whether increased attendance throughout the semester leads to improved exam scores. Let µ I = mean score that would be observed if all students used the interactive tool and µ E = mean score if all students worked an extra problem. The degrees of freedom, using a t table…
Joe and Maggie take turns mowing the lawn each week. Maggie suggests they try a new system for determining who should mow the lawn. Each week, they will roll two dice and determine the sum of the values. Since the highest possible sum is 12, Maggie will mow the lawn if the sum is 6 or less, and Joe will mow the lawn if the sum is greater than 6. Before agreeing to Maggie's suggestion, Joe wants to check if this plan would be fair. He decides to roll a pair of dice and determine the sum of the values 100 times. The graph shows the results of the 100 trials. Based on his simulation, should Joe agree to Maggie’s plan? (yes/no), because a sum greater than 6 is likely to occur (more than, less then, equal to)(30%, 50%, 75%) of the time
A shoe company wants to determine if the new tread on its top line of running shoes lasts longer than the original tread. The company recruits 50 runners for a study. Each runner will perform their typical workout wearing one shoe with the original tread on one foot and another shoe with the new tread on the other foot. The foot that wears the new type of tread will be decided by flipping a coin. After one month, the runner will wear the new type of tread on the opposite foot. At the end of the second month, the difference in tread wear (New – Original) will be calculated. What type of sampling is described in this study? What is the appropriate inference procedure? one-sample t-test for one-sample z-test for p one-sample t-test for two-sample t-test for
In this game, two chips are placed in a cup. One chip has two red sides and one chip has a red and a blue side. The player shakes the cup and dumps out the chips. The player wins if both chips land red side up and loses if one chip lands red side up and one chip lands blue side up. The cost to play is $4 and the prize is worth $6. Is this a fair game.
You need to borrow money for gas, so you ask your mother and your sister. You can only borrow money from one of them. Before giving you money, they each say they will make you play a game. Your sister says she wants you to flip a fair coin. She will give you $8$ for heads and $⁢22 for tails. Your mother says she wants you to roll a six-sided die. She will give you $4$ times the number that appears on the die. Determine the expected value of each game and decide which offer you should take.
You are a contestant on a game show. There are three closed doors in front of you. The game show host tells you that behind one of these doors is a million dollars in cash, and that behind the other two doors there are trashes. You do not know which doors contain which prizes, but the game show host does. The game you are going to play is very simple: you pick one of the three doors and win the prize behind it. After you have made your selection, the game show host opens one of the two doors that you did not choose and reveals trash. At this point, you are given the option to either stick with your original door or switch your choice to the only remaining closed door. To maximize your chance to win a million dollars in cash, should you switch? Choices: A) Yes B) No C) It doesn't matter because the probability for you to win a million dollars in cash stays the same no matter if you switch or not.
At your local carnival, there is a game where 40 rubber duckies are floating in a kiddie tub, and they each have their bottoms painted one of three colors. 55 are painted pink, 16 are painted blue, and 19 are painted purple. If the player selects a duck with a pink bottom, they receive three pieces of candy. If they select blue, they receive two pieces of candy. And if they select purple, they receive one piece of candy. If the game is played 42 times, what are the minimum and maximum amounts of candy that could be handed out?
You need to borrow money for gas, so you ask your mother and your sister. You can only borrow money from one of them. Before giving you money, they each say they will make you play a game. Your sister says she wants you to roll a six-sided die. She will give you $⁢4 times the number that appears on the die. Your mother says she wants you to spin a spinner with two outcomes, blue and red, on it. She will give you $⁢5 if the spinner lands on blue and $⁢15 if the spinner lands on red. Determine the expected value of each game and decide which offer you should take. The expected value for your sister's game: $$ The expected value for your mother's game: $$ Which offer should you take?
A researcher believed that the number of rental cars in service by a car rental company would have an impact on the total annual revenue for that car rental company. Five small car rental companies were surveyed, with the number of Cars in service recorded in units of 1000 (so if a car rental company had 54000 cars in service, a 54 would be recorded) and Annual Revenue measured in millions of dollars (so an Annual Revenue of $10,000,000 would be recorded as 10). The data follows: Cars (1,000s) Annual Revenue ($ millions)11.5 118 10.0 135 9.0 100 5.5 37 3.3 32 Part of the Excel-generated Simple Linear Regression output is provided below: ANOVA df SS MS F Significance F Regression 1 7891.863897 7891.863897 22.91180151 0.017339231 Residual 3 1033.336103 344.4453677 Total 4 8925.2 Coefficients Standard Error t Stat P-value Intercept -19.12490108 23.1658578…
You are using cash to pay a $20 parking ticket. In your wallet you have one $5-dollar bill, three $10-dollar bills, and two $20 dollar bills, and you draw out one bill at a time at random until you have at least $20. If you keep track of each bill as you draw it out of the wallet, how many different ways are there for you to get at least $20?
The past records of a supermarket show that its customers spend an average of $110 per visit at this store. Recently the management of the store initiated a promotional campaign according to which each customer receives points based on the total money spent at the store, and these points can be used to buy products at the store. The management expects that as a result of this campaign, the customers should be encouraged to spend more money at the store. To check whether this is true, the manager of the store took a sample of 14 customers who visited the store. The following data give the money (in dollars) spent by these customers at this supermarket during their visits. 106.13 107.43 124.68 124.88 101.17 72.75 85.45 86.05 100.4 98.84 101.63 95.56 89.40 119.52 Assume that the money spent by all customers at this supermarket has a normal distribution. Using a 2.5% significance level, can you conclude that the mean amount of money spent by all customers at this supermarket after the…

SEE MORE QUESTIONS

Recommended textbooks for you

A First Course in Probability (10th Edition)

Probability

ISBN:

9780134753119

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability

Probability

ISBN:

9780321794772

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability (10th Edition)

Probability

ISBN:

9780134753119

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability

Probability

ISBN:

9780321794772

Author:

Sheldon Ross

Publisher:

PEARSON

SEE MORE TEXTBOOKS