Derive a Markov chain to compute the probability of winning for the game of craps and compute the expected number of throws in craps.
Derive a Markov chain to compute the probability of winning for the game of craps and compute the expected number of throws in craps.
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter12: Probability
Section12.3: Conditional Probability; Independent Events; Bayes' Theorem
Problem 42E
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Question
Derive a Markov chain to compute the
Expert Solution
Step 1
Player rolls 2 dices simultaneously and the sum of numbers on the faces of the two dices determine whether the player wins, loses or continues to play.
There are 36 possible combinations of dices and the sum will range from 2 to 12.
Dice 1 | Dice 2 | Sum |
1 | 1 | 2 |
2 | 1 | 3 |
1 | 2 | 3 |
3 | 1 | 4 |
2 | 2 | 4 |
1 | 3 | 4 |
4 | 1 | 5 |
3 | 2 | 5 |
2 | 3 | 5 |
1 | 4 | 5 |
5 | 1 | 6 |
4 | 2 | 6 |
3 | 3 | 6 |
2 | 4 | 6 |
1 | 5 | 6 |
6 | 1 | 7 |
5 | 2 | 7 |
4 | 3 | 7 |
3 | 4 | 7 |
2 | 5 | 7 |
1 | 6 | 7 |
6 | 2 | 8 |
5 | 3 | 8 |
4 | 4 | 8 |
3 | 5 | 8 |
2 | 6 | 8 |
6 | 3 | 9 |
5 | 4 | 9 |
4 | 5 | 9 |
3 | 6 | 9 |
6 | 4 | 10 |
5 | 5 | 10 |
4 | 6 | 10 |
6 | 5 | 11 |
5 | 6 | 11 |
6 | 6 | 12 |
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