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 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 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
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 58E
Related questions
Question
Hi this solution was already posted on your website if you could just copy-paste the answer that would be nice.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 4 steps with 1 images
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
Holt Mcdougal Larson Pre-algebra: Student Edition…
Algebra
ISBN:
9780547587776
Author:
HOLT MCDOUGAL
Publisher:
HOLT MCDOUGAL
Algebra: Structure And Method, Book 1
Algebra
ISBN:
9780395977224
Author:
Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:
McDougal Littell