Answered: Derive a Markov chain to compute the…

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.7: Cooridinates And Change Of Basis

Problem 58E

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Question

Derive a Markov chain to compute the probability of winning for the game of craps and compute the expected number of throws in craps.

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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