Explanation Given: The matrix B started with $ 3 . Explanation: Consider the two players A and B , and the total amount is $5. Let player A start the game with the amount 0 , 1 , 2 , 3 , 4 , and 5 dollars. The amount of money held by player A is 0 , 1 , 2 , 3 , and 4 . If a player A reached either 0 or 1 , the game was over. When the amount is increased and decreased by the amount 1 after predicting the toss. If the toss is fare. Player B has a probability of 3 5 to win the toss. So, the probability of A to win the toss is: 1 − 3 5 = 2 5 The transition matrix P is P = [ 1 0 0 0 0 0 3 5 0 2 5 0 0 0 0 3 5 0 2 5 0 0 0 0 3 5 0 2 5 0 0 0 0 3 5 1 2 5 0 0 0 0 0 1 ] Now, write the matrix into the form of fundamental matrix. [ 1 0 0 0 0 0 0 1 0 0 0 0 3 5 0 0 2 5 0 0 0 0 3 5 0 2 5 0 0 0 0 3 5 0 2 5 0 2 5 0 0 3 5 0 ] Compare the matrix with [ I 2 O R Q ] Then, R = [ 3 5 0 0 0 0 0 2 5 ] The matrix Q = [ 0 2 5 0 0 3 5 0 2 5 0 0 3 5 0 2 5 0 0 3 5 0 ] Now, compute the fundamental matrix (a) To determine The probability that matrix A will be ruined when B starts with $ 3 . (b) To determine The probability that matrix A will be ruined when B starts with $ 1 .

11th Edition

ISBN: 9780321979438

Author: Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey

Publisher: PEARSON

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Chapter 10.3, Problem 16E

To determine

The probability of matrix A will be ruined if B starts with $3.

(a)

To determine

To determine : The probability that matrix A will be ruined when B starts with $3.

(b)

To determine

To determine : The probability that matrix A will be ruined when B starts with $1.

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Chapter 10.3, Problem 15E

Chapter 10.3, Problem 17E

Chapter 10 Solutions

Finite Mathematics (11th Edition)

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The probability of matrix A will be ruined if B starts with $3.

To determine : The probability that matrix A will be ruined when B starts with $3.

To determine : The probability that matrix A will be ruined when B starts with $1.

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