Bundle: Introduction to Statistics and Data Analysis, 5th + WebAssign Printed Access Card: Peck/Olsen/Devore. 5th Edition, Single-Term
5th Edition
ISBN: 9781305620711
Author: Roxy Peck, Chris Olsen, Jay L. Devore
Publisher: Cengage Learning
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Question
Chapter 6, Problem 94CR
a.
To determine
Compute the
b.
To determine
Find the probability that just five games needed to obtain a champion.
c.
To determine
Explain the way of performing simulation to estimate the probability that A wins the championship.
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Two individuals, A and B,are finalists for a chess championship. They will play a sequence of games, each of which can result in a win for A, a win for B, or a draw. Suppose that the outcomes of successive games are independent, with P(A wins game) .3, P(B wins game) .2, and P(draw) .5. Each time a player wins a game, he earns 1 point and his opponent earns no points. The first player to win 5 points wins the championship. For the sake of simplicity, assume that the championship will end in a draw if both players obtain 5 points at the same time.
a. What is the probability that A wins the championship in just five games?b. What is the probability that it takes just five games to obtain a champion?
c. Ifadrawearnsahalf-pointforeachplayer,describe how you would perform a simulation to estimate P(A wins the championship).d. If neither player earns any points from a draw, would the simulation in Part (c) take longer to perform? Explain your reasoning.
Players A and B play a sequence of independent games. Player A throwsa die first and wins on a “six.” If he fails, B throws and wins on a “five” or “six.”If he fails, A throws and wins on a “four,” “five,” or “six.” And so on. Find theprobability of each player winning the sequence.
Bob and Doug play a lot of Ping-Pong, but Doug is a much better player, and wins 60% 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 spot Bob ten points the next game, and if he still wins the next game he will spot him
fifteen points, and continue to spot him fifteen points as long as he keeps winning. Whenever Bob wins a game he goes back to playing the next game with no advantage.
It turns out that with a five-point advantage Bob wins 70% of the time; he wins 80% of the time with a ten-point advantage and 90% 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 should be four states representing zero, one, two, and three or more consecutive game
won by Doug. Find the transition matrix of this system, the steady-state vector for the system, and determine the proportion of games that Doug will win in…
Chapter 6 Solutions
Bundle: Introduction to Statistics and Data Analysis, 5th + WebAssign Printed Access Card: Peck/Olsen/Devore. 5th Edition, Single-Term
Ch. 6.1 - Define the term chance experiment, and give an...Ch. 6.1 - Define the term sample space, and then give the...Ch. 6.1 - Consider the chance experiment in which the type...Ch. 6.1 - A tennis shop sells five different brands of...Ch. 6.1 - A new model of laptop computer can be ordered with...Ch. 6.1 - A college library has four copies of a certain...Ch. 6.1 - A library has five copies of a certain textbook on...Ch. 6.1 - Suppose that, starting at a certain time,...Ch. 6.1 - Refer to the previous exercise and now suppose...Ch. 6.1 - Prob. 10E
Ch. 6.1 - An engineering construction firm is currently...Ch. 6.1 - Consider a Venn diagram picturing two events A and...Ch. 6.3 - A large department store offers online ordering....Ch. 6.3 - The manager of a music store has kept records of...Ch. 6.3 - A bookstore sells two types of books (fiction and...Ch. 6.3 - ▼ Medical insurance status—covered (C) or not...Ch. 6.3 - Roulette is a game of chance that involves...Ch. 6.3 - Phoenix is a hub for a large airline. Suppose that...Ch. 6.3 - A professor assigns five problems to be completed...Ch. 6.3 - Refer to the following information on full-term...Ch. 6.3 - Prob. 21ECh. 6.3 - Prob. 22ECh. 6.3 - Prob. 23ECh. 6.3 - Prob. 24ECh. 6.3 - A deck of 52 playing cards is mixed well, and 5...Ch. 6.3 - Prob. 26ECh. 6.3 - The student council for a school of science and...Ch. 6.3 - A student placement center has requests from five...Ch. 6.3 - Prob. 29ECh. 6.4 - Two different airlines have a flight from Los...Ch. 6.4 - The article Chances Are You Know Someone with a...Ch. 6.4 - The accompanying data are from the article...Ch. 6.4 - The following graphical display is similar to one...Ch. 6.4 - Delayed diagnosis of cancer is a problem because...Ch. 6.4 - The events E and T are defined as E = the event...Ch. 6.4 - The newspaper article Folic Acid Might Reduce Risk...Ch. 6.4 - Suppose that an individual is randomly selected...Ch. 6.4 - Is ultrasound a reliable method for determining...Ch. 6.4 - The table at the top of the next page summarizes...Ch. 6.4 - USA Today (June 6, 2000) gave information on seal...Ch. 6.4 - Prob. 41ECh. 6.4 - The paper Good for Women, Good for Men, Bad for...Ch. 6.5 - Many fire stations handle emergency calls for...Ch. 6.5 - The paper Predictors of Complementary Therapy Use...Ch. 6.5 - The report TV Drama/Comedy Viewers and Health...Ch. 6.5 - Prob. 46ECh. 6.5 - Prob. 47ECh. 6.5 - In a small city, approximately 15% of those...Ch. 6.5 - Jeanie is a bit forgetful, and if she doesnt make...Ch. 6.5 - Prob. 50ECh. 6.5 - Prob. 51ECh. 6.5 - Prob. 52ECh. 6.5 - The following case study was reported in the...Ch. 6.5 - Three friends (A, B, and C) will participate in a...Ch. 6.5 - Prob. 55ECh. 6.5 - A store sells two different brands of dishwasher...Ch. 6.5 - The National Public Radio show Car Talk used to...Ch. 6.5 - Refer to the previous exercise. Suppose now that...Ch. 6.6 - A university has 10 vehicles available for use by...Ch. 6.6 - Prob. 60ECh. 6.6 - Prob. 61ECh. 6.6 - Let F denote the event that a randomly selected...Ch. 6.6 - According to a July 31, 2013 posting on cnn.com, a...Ch. 6.6 - Suppose that Blue Cab operates 15% of the taxis in...Ch. 6.6 - A large cable company reports the following: 80%...Ch. 6.6 - Refer to the information given in the previous...Ch. 6.6 - The authors of the paper Do Physicians Know When...Ch. 6.6 - A study of how people are using online services...Ch. 6.6 - Prob. 69ECh. 6.6 - Prob. 70ECh. 6.6 - Prob. 71ECh. 6.6 - Prob. 72ECh. 6.6 - Prob. 73ECh. 6.6 - The paper referenced in the previous exercise also...Ch. 6.6 - In an article that appears on the web site of the...Ch. 6.6 - Prob. 76ECh. 6.6 - Only 0.1% of the individuals in a certain...Ch. 6.7 - The Los Angeles Times (June 14, 1995) reported...Ch. 6.7 - Five hundred first-year students at a state...Ch. 6.7 - The table given below describes (approximately)...Ch. 6.7 - On April 1, 2010, the Bureau of the Census in the...Ch. 6 - A company uses three different assembly linesA1,...Ch. 6 - Prob. 88CRCh. 6 - Prob. 89CRCh. 6 - Prob. 90CRCh. 6 - Prob. 91CRCh. 6 - A company sends 40% of its overnight mail parcels...Ch. 6 - Prob. 93CRCh. 6 - Prob. 94CRCh. 6 - In a school machine shop, 60% of all machine...Ch. 6 - There are five faculty members in a certain...Ch. 6 - The general addition rule for three events states...Ch. 6 - A theater complex is currently showing four...Ch. 6 - Prob. 100CRCh. 6 - Suppose that a box contains 25 light bulbs, of...Ch. 6 - Prob. 102CRCh. 6 - A transmitter is sending a message using a binary...
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- Bob and Doug play a lot of Ping-Pong, but Doug is a much better player, and wins 60% 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 spot Bob ten points the next game, and if he still wins the next game he will spot him fifteen points, and continue to spot him fifteen points as long as he keeps winning. Whenever Bob wins a game he goes back to playing the next game with no advantage. It turns out that with a five-point advantage Bob wins 40% of the time; he wins 70% of the time with a ten-point advantage and 70% 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 should be four states representing zero, one, two, and three or more consecutive games won by Doug. Find the transition matrix of this system, the steady-state vector for the system, and determine the proportion of games that Doug will win in…arrow_forwardBob and Doug play a lot of Ping-Pong, but Doug is a much better player, and wins 60% 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 spot Bob ten points the next game, and if he still wins the next game he will spot him fifteen points, and continue to spot him fifteen points as long as he keeps winning. Whenever Bob wins a game he goes back to playing the next game with no advantage.It turns out that with a five-point advantage Bob wins 60% of the time; he wins 70% of the time with a ten-point advantage and 90% 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 should be four states representing zero, one, two, and three or more consecutive games won by Doug. Find the transition matrix of this system, the steady-state vector for the system, and determine the proportion of games that Doug will win in the…arrow_forwardBob and Doug play a lot of Ping-Pong, but Doug is a much better player, and wins 60% 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 spot Bob ten points the next game, and if he still wins the next game he will spot him fifteen points, and continue to spot him fifteen points as long as he keeps winning. Whenever Bob wins a game he goes back to playing the next game with no advantage.It turns out that with a five-point advantage Bob wins 60% of the time; he wins 60% of the time with a ten-point advantage and 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 should be four states representing zero, one, two, and three or more consecutive games won by Doug. Find the transition matrix of this system, the steady-state vector for the system, and determine the proportion of games that Doug will win in the…arrow_forward
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