Major League Baseball's World Series is a maximum of seven games, with the winner being the first team to win four games. Assume that the Atlanta Braves and the Minnesota Twins are playing in the World Series and that the first two games are to be played in Atlanta, the next three games at the Twins' ballpark, and the last two games, if necessary, back in Atlanta. Taking into account the projected starting pitchers for each game and the home field advantage, suppose the probabilities of Atlanta winning each game are as follows. Game 1 2 3 4 5 6 7 Probability of Win 0.59 0.56 0.47 0.44 0.49 0.54 0.51 Construct a simulation model in which whether Atlanta wins or loses each game is a random variable. Use the model to answer the following questions. (Use at least 1,000 trials.) (a) What is the average number of games played regardless of winner? (Round your answer to one decimal place.) games (b) What is the probability that the Atlanta Braves win the World Series? (Round your answer to three decimal places.)
Major League Baseball's World Series is a maximum of seven games, with the winner being the first team to win four games. Assume that the Atlanta Braves and the Minnesota Twins are playing in the World Series and that the first two games are to be played in Atlanta, the next three games at the Twins' ballpark, and the last two games, if necessary, back in Atlanta. Taking into account the projected starting pitchers for each game and the home field advantage, suppose the probabilities of Atlanta winning each game are as follows. Game 1 2 3 4 5 6 7 Probability of Win 0.59 0.56 0.47 0.44 0.49 0.54 0.51 Construct a simulation model in which whether Atlanta wins or loses each game is a random variable. Use the model to answer the following questions. (Use at least 1,000 trials.) (a) What is the average number of games played regardless of winner? (Round your answer to one decimal place.) games (b) What is the probability that the Atlanta Braves win the World Series? (Round your answer to three decimal places.)
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...
Related questions
Question
100%
please show me step by step, I have been stuck for hours, need to learn the steps
Transcribed Image Text:**Major League Baseball's World Series Overview**
The World Series is a best-of-seven games competition. The winner is the first team to win four games. In this scenario, the Atlanta Braves and the Minnesota Twins are competing. The series is structured with the first two games played in Atlanta, the subsequent three games at the Twins' ballpark, and the final two games, if necessary, back in Atlanta. The probabilities of Atlanta winning each game are influenced by projected starting pitchers and home field advantage. These probabilities are outlined in the table below:
| Game | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
|-----------------------|-----|-----|-----|-----|-----|-----|-----|
| Probability of Win | 0.59 | 0.56 | 0.47 | 0.44 | 0.49 | 0.54 | 0.51 |
**Simulation Model Tasks**
Create a simulation model to determine the outcome of each game as a random variable. Utilize this model to answer the following questions through at least 1,000 trials:
(a) **Average Number of Games Played:**
Determine the average number of games played, irrespective of the winner. Please round your answer to one decimal place.
(b) **Probability of Atlanta Braves Winning:**
Calculate the probability of the Atlanta Braves winning the World Series. Round your answer to three decimal places.
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 5 steps with 5 images
Recommended textbooks for you
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON