Finite Mathematics, Books a la Carte Plus MyLab Math Access Card Package (11th Edition)
11th Edition
ISBN: 9780133886818
Author: Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Videos
Textbook Question
Chapter 10.3, Problem 15E
(a) Write a transition matrix for a gambler's ruin problem when player A and player B start with a total of $4. (See Example 2.)
(b) Find matrix F for this transition matrix, and find the product matrix FR.
(c) Suppose player A starts with $1. What is the probability of ruin for A?
(d) Suppose player A starts with $3. What is the probability of ruin for A?
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Page <
1
of 2
-
ZOOM +
1) a) Find a matrix P such that PT AP orthogonally diagonalizes the following matrix
A.
= [{² 1]
A =
b) Verify that PT AP gives the correct diagonal form.
2
01
-2
3
2) Given the following matrices A =
-1
0
1] an
and B =
0
1
-3
2
find the following matrices:
a) (AB) b) (BA)T
3) Find the inverse of the following matrix A using Gauss-Jordan elimination or
adjoint of the matrix and check the correctness of your answer (Hint: AA¯¹ = I).
[1 1 1
A = 3 5 4
L3 6 5
4) Solve the following system of linear equations using any one of Cramer's Rule,
Gaussian Elimination, Gauss-Jordan Elimination or Inverse Matrix methods and
check the correctness of your answer.
4x-y-z=1
2x + 2y + 3z = 10
5x-2y-2z = -1
5) a) Describe the zero vector and the additive inverse of a vector in the vector
space, M3,3.
b) Determine if the following set S is a subspace of M3,3 with the standard
operations. Show all appropriate supporting work.
13) Let U = {j, k, l, m, n, o, p} be the universal set. Let V = {m, o,p), W = {l,o, k}, and X = {j,k). List the elements of
the following sets and the cardinal number of each set.
a) W° and n(W)
b) (VUW) and n((V U W)')
c) VUWUX and n(V U W UX)
d) vnWnX and n(V WnX)
9) Use the Venn Diagram given below to determine the number elements in each of the following sets.
a) n(A).
b) n(A° UBC).
U
B
oh
a
k
gy
ท
W
z r
e t
་
C
Chapter 10 Solutions
Finite Mathematics, Books a la Carte Plus MyLab Math Access Card Package (11th Edition)
Ch. 10.1 -
Decide whether each matrix could be a...Ch. 10.1 - Decide whether each matrix could be a probability...Ch. 10.1 - Prob. 3ECh. 10.1 - Prob. 4ECh. 10.1 - Decide whether each matrix could be a probability...Ch. 10.1 -
Decide whether each matrix could be a...Ch. 10.1 - Prob. 7ECh. 10.1 - Prob. 8ECh. 10.1 - Decide whether each matrix could be a transition...Ch. 10.1 -
Decide whether each matrix could be a...
Ch. 10.1 - Prob. 11ECh. 10.1 - Prob. 12ECh. 10.1 - Prob. 13ECh. 10.1 - Prob. 14ECh. 10.1 - In Exercises and 16, write each transition diagram...Ch. 10.1 - Prob. 16ECh. 10.1 - Prob. 17ECh. 10.1 - Prob. 18ECh. 10.1 - Prob. 19ECh. 10.1 -
Find the first three powers of each transition...Ch. 10.1 - Prob. 21ECh. 10.1 - Prob. 22ECh. 10.1 - Prob. 23ECh. 10.1 - Prob. 24ECh. 10.1 - Prob. 25ECh. 10.1 - Prob. 26ECh. 10.1 - Prob. 27ECh. 10.1 - Insurance An insurance company classifies its...Ch. 10.1 -
Insurance The difficulty with the mathematical...Ch. 10.1 - Prob. 30ECh. 10.1 - Prob. 31ECh. 10.1 -
32. Land Use In one state, a Board of Realtors...Ch. 10.1 - Business The change in the size of businesses in a...Ch. 10.1 - Prob. 34ECh. 10.1 - Prob. 35ECh. 10.1 - Housing Patterns In a survey investigating changes...Ch. 10.1 - Migration A study found that the way people living...Ch. 10.1 - Prob. 38ECh. 10.1 - Prob. 39ECh. 10.2 -
Which of the following transition matrices are...Ch. 10.2 -
Which of the following transition matrices are...Ch. 10.2 -
Which of the following transition matrices are...Ch. 10.2 - Prob. 4ECh. 10.2 - Prob. 5ECh. 10.2 - Prob. 6ECh. 10.2 - Prob. 7ECh. 10.2 - Prob. 8ECh. 10.2 - Prob. 9ECh. 10.2 - Prob. 10ECh. 10.2 -
Find the equilibrium vector for each transition...Ch. 10.2 - Prob. 12ECh. 10.2 - Prob. 13ECh. 10.2 - Prob. 14ECh. 10.2 - Find the equilibrium vector for each transition...Ch. 10.2 - Prob. 16ECh. 10.2 -
Find the equilibrium vector for each...Ch. 10.2 - Prob. 18ECh. 10.2 - Prob. 19ECh. 10.2 - Prob. 20ECh. 10.2 - Prob. 21ECh. 10.2 - Prob. 22ECh. 10.2 - Prob. 23ECh. 10.2 - Prob. 24ECh. 10.2 - Business and Economics Quality Control The...Ch. 10.2 -
26. Quality Control Suppose improvements are made...Ch. 10.2 - (a) Dry Cleaning Using the initial probability...Ch. 10.2 - Mortgage Refinancing In 2009, many homeowners...Ch. 10.2 - Prob. 29ECh. 10.2 - Prob. 30ECh. 10.2 - Prob. 31ECh. 10.2 - Prob. 32ECh. 10.2 - Prob. 33ECh. 10.2 - Prob. 34ECh. 10.2 - Migration As we saw in the last section, a study...Ch. 10.2 -
36. Criminology A study male criminals in...Ch. 10.2 - Prob. 37ECh. 10.2 - Prob. 38ECh. 10.2 - Prob. 39ECh. 10.2 - Prob. 40ECh. 10.2 - Prob. 41ECh. 10.2 -
42. Language One of Markov's own applications...Ch. 10.2 - Prob. 43ECh. 10.2 - Prob. 44ECh. 10.3 - Find all absorbing states for each transition...Ch. 10.3 - Find all absorbing states for each transition...Ch. 10.3 -
Find all absorbing states for each transition...Ch. 10.3 - Find all absorbing states for each transition...Ch. 10.3 -
Find all absorbing states for each transition...Ch. 10.3 - Find all absorbing states for each transition...Ch. 10.3 - Prob. 7ECh. 10.3 - Prob. 8ECh. 10.3 -
Find the fundamental matrix F for the absorbing...Ch. 10.3 - Prob. 10ECh. 10.3 -
Find the fundamental matrix F for the absorbing...Ch. 10.3 - Find the fundamental matrix F for the absorbing...Ch. 10.3 - Prob. 13ECh. 10.3 - Prob. 14ECh. 10.3 - (a) Write a transition matrix for a gambler's ruin...Ch. 10.3 - Prob. 16ECh. 10.3 - Prob. 17ECh. 10.3 - Prob. 18ECh. 10.3 - Prob. 19ECh. 10.3 -
20. How can we calculate the expected total...Ch. 10.3 - Prob. 21ECh. 10.3 - Prob. 22ECh. 10.3 -
Business and Economics
23. Solar Energy In...Ch. 10.3 -
24. Company Training Program A company with a...Ch. 10.3 - Contagion Under certain conditions, the...Ch. 10.3 - 26. Medical Prognosis A study using Markov chains...Ch. 10.3 - Prob. 27ECh. 10.3 - Prob. 28ECh. 10.3 - Prob. 29ECh. 10.3 - Prob. 30ECh. 10.3 - Gambler's Ruin (a) Write a transition matrix tor a...Ch. 10.3 -
32. Tennis Consider a game of tennis when each...Ch. 10.3 - Professional Football In Exercise 40 of the first....Ch. 10 -
1. If a teacher is currently ill, what is the...Ch. 10 - Prob. 2EACh. 10 - Prob. 3EACh. 10 - Prob. 4EACh. 10 - Prob. 5EACh. 10 - Prob. 6EACh. 10 - Prob. 7EACh. 10 - Prob. 1RECh. 10 - Prob. 2RECh. 10 - Prob. 3RECh. 10 - Prob. 4RECh. 10 - Prob. 5RECh. 10 - Prob. 6RECh. 10 - Prob. 7RECh. 10 - Prob. 8RECh. 10 - Prob. 9RECh. 10 - Prob. 10RECh. 10 - Prob. 11RECh. 10 - Prob. 12RECh. 10 - Prob. 13RECh. 10 - Prob. 14RECh. 10 - Prob. 15RECh. 10 - Prob. 16RECh. 10 - Prob. 17RECh. 10 - Prob. 18RECh. 10 - Prob. 19RECh. 10 - Prob. 20RECh. 10 - Prob. 21RECh. 10 - Prob. 22RECh. 10 - Prob. 23RECh. 10 - Prob. 24RECh. 10 - Prob. 25RECh. 10 - In Exercises 23-26, use the transition matrix P,...Ch. 10 - Prob. 27RECh. 10 - Prob. 28RECh. 10 - Prob. 29RECh. 10 - Decide whether each transition matrix is regular....Ch. 10 - Prob. 31RECh. 10 - Prob. 32RECh. 10 - Prob. 33RECh. 10 - Prob. 34RECh. 10 - Prob. 35RECh. 10 - Find all absorbing states for each matrix. Which...Ch. 10 - Prob. 37RECh. 10 - Prob. 38RECh. 10 - Prob. 39RECh. 10 - Prob. 40RECh. 10 - Prob. 41RECh. 10 - Prob. 42RECh. 10 - Prob. 43RECh. 10 - Prob. 44RECh. 10 - Prob. 45RECh. 10 - Prob. 46RECh. 10 - Prob. 47RECh. 10 - Prob. 48RECh. 10 -
Life Sciences
49. Medical Prognosis A study...Ch. 10 - Prob. 50RECh. 10 - Prob. 51RECh. 10 - Prob. 52RECh. 10 - Prob. 53RECh. 10 - Prob. 54RECh. 10 - Prob. 55RECh. 10 - Prob. 56RECh. 10 - Prob. 57RECh. 10 - Prob. 58RECh. 10 - Prob. 59RECh. 10 - Prob. 60RECh. 10 - Prob. 61RECh. 10 - Prob. 62RECh. 10 - Prob. 63RECh. 10 - Prob. 64RECh. 10 - Prob. 65RECh. 10 - Prob. 66RECh. 10 - Prob. 67RECh. 10 - Prob. 68RECh. 10 -
69. Gambling Suppose a casino offers a gambling...
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.Similar questions
- 10) Find n(K) given that n(T) = 7,n(KT) = 5,n(KUT) = 13.arrow_forward7) Use the Venn Diagram below to determine the sets A, B, and U. A = B = U = Blue Orange white Yellow Black Pink Purple green Grey brown Uarrow_forward8. For x>_1, the continuous function g is decreasing and positive. A portion of the graph of g is shown above. For n>_1, the nth term of the series summation from n=1 to infinity a_n is defined by a_n=g(n). If intergral 1 to infinity g(x)dx converges to 8, which of the following could be true? A) summation n=1 to infinity a_n = 6. B) summation n=1 to infinity a_n =8. C) summation n=1 to infinity a_n = 10. D) summation n=1 to infinity a_n diverges.arrow_forward
- 1) Use the roster method to list the elements of the set consisting of: a) All positive multiples of 3 that are less than 20. b) Nothing (An empty set).arrow_forward2) Let M = {all postive integers), N = {0,1,2,3... 100), 0= {100,200,300,400,500). Determine if the following statements are true or false and explain your reasoning. a) NCM b) 0 C M c) O and N have at least one element in common d) O≤ N e) o≤o 1arrow_forward4) Which of the following universal sets has W = {12,79, 44, 18) as a subset? Choose one. a) T = {12,9,76,333, 44, 99, 1000, 2} b) V = {44,76, 12, 99, 18,900,79,2} c) Y = {76,90, 800, 44, 99, 55, 22} d) x = {79,66,71, 4, 18, 22,99,2}arrow_forward
- 3) What is the universal set that contains all possible integers from 1 to 8 inclusive? Choose one. a) A = {1, 1.5, 2, 2.5, 3, 3.5, 4, 4.5, 5, 5.5, 6, 6.5, 7, 7.5, 8} b) B={-1,0,1,2,3,4,5,6,7,8} c) C={1,2,3,4,5,6,7,8} d) D = {0,1,2,3,4,5,6,7,8}arrow_forwardA smallish urn contains 25 small plastic bunnies – 7 of which are pink and 18 of which are white. 10 bunnies are drawn from the urn at random with replacement, and X is the number of pink bunnies that are drawn. (a) P(X = 5) ≈ (b) P(X<6) ≈ The Whoville small urn contains 100 marbles – 60 blue and 40 orange. The Grinch sneaks in one night and grabs a simple random sample (without replacement) of 15 marbles. (a) The probability that the Grinch gets exactly 6 blue marbles is [ Select ] ["≈ 0.054", "≈ 0.043", "≈ 0.061"] . (b) The probability that the Grinch gets at least 7 blue marbles is [ Select ] ["≈ 0.922", "≈ 0.905", "≈ 0.893"] . (c) The probability that the Grinch gets between 8 and 12 blue marbles (inclusive) is [ Select ] ["≈ 0.801", "≈ 0.760", "≈ 0.786"] . The Whoville small urn contains 100 marbles – 60 blue and 40 orange. The Grinch sneaks in one night and grabs a simple random sample (without replacement) of 15 marbles. (a)…arrow_forwardUsing Karnaugh maps and Gray coding, reduce the following circuit represented as a table and write the final circuit in simplest form (first in terms of number of gates then in terms of fan-in of those gates).arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Elementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage Learning
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:9781305658004
Author:Ron Larson
Publisher:Cengage Learning
Finite Math: Markov Chain Example - The Gambler's Ruin; Author: Brandon Foltz;https://www.youtube.com/watch?v=afIhgiHVnj0;License: Standard YouTube License, CC-BY
Introduction: MARKOV PROCESS And MARKOV CHAINS // Short Lecture // Linear Algebra; Author: AfterMath;https://www.youtube.com/watch?v=qK-PUTuUSpw;License: Standard Youtube License
Stochastic process and Markov Chain Model | Transition Probability Matrix (TPM); Author: Dr. Harish Garg;https://www.youtube.com/watch?v=sb4jo4P4ZLI;License: Standard YouTube License, CC-BY