Homework Help is Here – Start Your Trial Now!
Math
Probability
15 Stick or Roll Stick or roll is a game involving two players, A and B, and a die with four faces (numbered 1, 2, 3, 4). The faces are equally likely to occur when the die is rolled. Player A rolls the die once and sticks with that number as the score or rolls it again and scores the sum of the two numbers. • If A's score is greater than 4 then A loses. • If A's score is 4 then A wins. If A's score is less than 4, then B rolls the die once and sticks with that number as the score or rolls it again and scores the sum of the two numbers. • If B's score is greater than 4 then B loses. • If B's score is 4 or less and equal to A's or less, then B loses. • If B's score is 4 or less and greater than A's, then B wins. Player B sticks on the first roll if that number wins and rolls again if it doesn't win and it is possible to win with a second roll. Some example games might be: * A rolls a 2, chooses to roll again and rolls a 3. A's score is then 5 so A loses and B wins. * A rolls a 2 and chooses not to roll again. B rolls a 2, so rolls again and rolls another 2. B's score is then 4, so B wins. * A rolls a 1, chooses to roll again and rolls a 2. B rolls a 2, rolls again and rolls a 3. B's score is then 5 so B loses and A wins. In solutions to the following questions express all probabilities exactly. a If A's score is 3, describe the ways in which B could win. b If A's score is 3, what is the probability that B wins? c If A's score is 2, what is the probability that B wins? d Player A decides to stick if the first roll is 3 or 4, otherwise rolls again. What is the probability that A wins the game using this strategy?

15 Stick or Roll Stick or roll is a game involving two players, A and B, and a die with four faces (numbered 1, 2, 3, 4). The faces are equally likely to occur when the die is rolled. Player A rolls the die once and sticks with that number as the score or rolls it again and scores the sum of the two numbers. • If A's score is greater than 4 then A loses. • If A's score is 4 then A wins. If A's score is less than 4, then B rolls the die once and sticks with that number as the score or rolls it again and scores the sum of the two numbers. • If B's score is greater than 4 then B loses. • If B's score is 4 or less and equal to A's or less, then B loses. • If B's score is 4 or less and greater than A's, then B wins. Player B sticks on the first roll if that number wins and rolls again if it doesn't win and it is possible to win with a second roll. Some example games might be: * A rolls a 2, chooses to roll again and rolls a 3. A's score is then 5 so A loses and B wins. * A rolls a 2 and chooses not to roll again. B rolls a 2, so rolls again and rolls another 2. B's score is then 4, so B wins. * A rolls a 1, chooses to roll again and rolls a 2. B rolls a 2, rolls again and rolls a 3. B's score is then 5 so B loses and A wins. In solutions to the following questions express all probabilities exactly. a If A's score is 3, describe the ways in which B could win. b If A's score is 3, what is the probability that B wins? c If A's score is 2, what is the probability that B wins? d Player A decides to stick if the first roll is 3 or 4, otherwise rolls again. What is the probability that A wins the game using this strategy?

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 58E
See similar textbooks
icon
Related questions
Question

Please can you solve B, C and D

15 Stick or Roll Stick or roll is a game involving two players, A and B, and a die with four faces (numbered 1, 2, 3, 4). The faces are equally likely to occur when the die is rolled. Player A rolls the die once and sticks with that number as the score or rolls it again and scores the sum of the two numbers. • If A's score is greater than 4 then A loses. • If A's score is 4 then A wins. If A's score is less than 4, then B rolls the die once and sticks with that number as the score or rolls it again and scores the sum of the two numbers. • If B's score is greater than 4 then B loses. • If B's score is 4 or less and equal to A's or less, then B loses. • If B's score is 4 or less and greater than A's, then B wins. Player B sticks on the first roll if that number wins and rolls again if it doesn't win and it is possible to win with a second roll. Some example games might be: * A rolls a 2, chooses to roll again and rolls a 3. A's score is then 5 so A loses and B wins. * A rolls a 2 and chooses not to roll again. B rolls a 2, so rolls again and rolls another 2. B's score is then 4, so B wins. * A rolls a 1, chooses to roll again and rolls a 2. B rolls a 2, rolls again and rolls a 3. B's score is then 5 so B loses and A wins. In solutions to the following questions express all probabilities exactly. a If A's score is 3, describe the ways in which B could win. b If A's score is 3, what is the probability that B wins? c If A's score is 2, what is the probability that B wins? d Player A decides to stick if the first roll is 3 or 4, otherwise rolls again. What is the probability that A wins the game using this strategy?
Transcribed Image Text:15 Stick or Roll Stick or roll is a game involving two players, A and B, and a die with four faces (numbered 1, 2, 3, 4). The faces are equally likely to occur when the die is rolled. Player A rolls the die once and sticks with that number as the score or rolls it again and scores the sum of the two numbers. • If A's score is greater than 4 then A loses. • If A's score is 4 then A wins. If A's score is less than 4, then B rolls the die once and sticks with that number as the score or rolls it again and scores the sum of the two numbers. • If B's score is greater than 4 then B loses. • If B's score is 4 or less and equal to A's or less, then B loses. • If B's score is 4 or less and greater than A's, then B wins. Player B sticks on the first roll if that number wins and rolls again if it doesn't win and it is possible to win with a second roll. Some example games might be: * A rolls a 2, chooses to roll again and rolls a 3. A's score is then 5 so A loses and B wins. * A rolls a 2 and chooses not to roll again. B rolls a 2, so rolls again and rolls another 2. B's score is then 4, so B wins. * A rolls a 1, chooses to roll again and rolls a 2. B rolls a 2, rolls again and rolls a 3. B's score is then 5 so B loses and A wins. In solutions to the following questions express all probabilities exactly. a If A's score is 3, describe the ways in which B could win. b If A's score is 3, what is the probability that B wins? c If A's score is 2, what is the probability that B wins? d Player A decides to stick if the first roll is 3 or 4, otherwise rolls again. What is the probability that A wins the game using this strategy?
Expert Solution
steps

Step by step

Solved in 3 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar questions
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
College Algebra
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Algebra and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:
9781305071742
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
College Algebra
College Algebra
Algebra
ISBN:
9781337282291
Author:
Ron Larson
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS