On any given day, a student is either healthy or ill. Of the students who are healthy today, 90% will be healthy tomorrow. Of the students who are ill today, 55% will still be ill tomorrow. Complete parts (a) and (b) below. a. Find the steady-state vector for the Markov chain described above. (Type an integer or simplified fraction for each matrix element.) b. What is the probability that after many days a specific student is ill? Does it matter if that person is ill today? Select the best choice below and fill in the answer box to complete your choice. (Round to the nearest hundredth as needed.) O A. The probability is . Yes, it does matter if that person is ill today. O B. The probability is No, it does not matter if that person is ill today.

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter2: Matrices
Section2.5: Markov Chain
Problem 55E
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12. On any given day, a student is either healthy or ill. Of the students who are healthy today, 90%
will be healthy tomorrow. Of the students who are ill today, 55% will still be ill tomorrow. Complete
parts (a) and (b) below.
a. Find the steady-state vector for the Markov chain described above.
q =
(Type an integer or simplified fraction for each matrix element.)
b. What is the probability that after many days a specific student is ill? Does it matter if that
person is ill today? Select the best choice below and fill in the answer box to complete your
choice.
(Round to the nearest hundredth as needed.)
O A. The probability is
Yes, it does matter if that person is ill today.
O B. The probability is
No, it does not matter if that person is ill today.
Transcribed Image Text:12. On any given day, a student is either healthy or ill. Of the students who are healthy today, 90% will be healthy tomorrow. Of the students who are ill today, 55% will still be ill tomorrow. Complete parts (a) and (b) below. a. Find the steady-state vector for the Markov chain described above. q = (Type an integer or simplified fraction for each matrix element.) b. What is the probability that after many days a specific student is ill? Does it matter if that person is ill today? Select the best choice below and fill in the answer box to complete your choice. (Round to the nearest hundredth as needed.) O A. The probability is Yes, it does matter if that person is ill today. O B. The probability is No, it does not matter if that person is ill today.
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