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In a population of 10,000, there are 5000 nonsmokers, 2500 smokers of one pack or less per day, and 2500 smokers of more than one pack per day. During any month, there is an 8% probability that a nonsmoker will begin smoking a pack or less per day, and a 4% probability that a nonsmoker will begin smoking more than a pack per day. For smokers who smoke a pack or less per day, there is a 10% probability of quitting and a 10% probability of increasing to more than a pack per day. For smokers who smoke more than a pack per day, there is a 7% probability of quitting and a 10% probability of dropping to a pack or less per day. How many people will be in each group in 1 month, in 2 months, and in 1 year? (Round your answers to the nearest whole number.) (a) in 1 month nonsmokers 4825 people 1 pack/day or less 2650 people more than 1 pack/day 2525 people (b) in 2 months 4687 25 2758 5 people people nonsmokers 1 pack/day or less more than 1 pack/day 2553.75 people (c) in 1 year people people people nonsmokers 1 pack/day or less more than 1 pack/day

In a population of 10,000, there are 5000 nonsmokers, 2500 smokers of one pack or less per day, and 2500 smokers of more than one pack per day. During any month, there is an 8% probability that a nonsmoker will begin smoking a pack or less per day, and a 4% probability that a nonsmoker will begin smoking more than a pack per day. For smokers who smoke a pack or less per day, there is a 10% probability of quitting and a 10% probability of increasing to more than a pack per day. For smokers who smoke more than a pack per day, there is a 7% probability of quitting and a 10% probability of dropping to a pack or less per day. How many people will be in each group in 1 month, in 2 months, and in 1 year? (Round your answers to the nearest whole number.) (a) in 1 month nonsmokers 4825 people 1 pack/day or less 2650 people more than 1 pack/day 2525 people (b) in 2 months 4687 25 2758 5 people people nonsmokers 1 pack/day or less more than 1 pack/day 2553.75 people (c) in 1 year people people people nonsmokers 1 pack/day or less more than 1 pack/day

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter2: Matrices
Section2.5: Markov Chain
Problem 15E: Smokers and Non smokers In a population of 10,000, there are 5000 non-smokers, 2500 smokers of one...
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Note:- Please need all the answers for Part a, b, c with a full explanation for this problem.

In a population of 10,000, there are 5000 nonsmokers, 2500 smokers of one pack or less per day, and 2500 smokers of more than one pack per day. During any month, there is an 8% probability that a nonsmoker will begin smoking a pack or less per day, and a 4% probability that a nonsmoker will begin smoking more than a pack per day. For smokers who smoke a pack or less per day, there is a 10% probability of quitting and a 10% probability of increasing to more than a pack per day. For smokers who smoke more than a pack per day, there is a 7% probability of quitting and a 10% probability of dropping to a pack or less per day. How many people will be in each group in 1 month, in 2 months, and in 1 year? (Round your answers to the nearest whole number.) (a) in 1 month nonsmokers 4825 реople 1 pack/day or less 2650 people more than 1 pack/day 2525 people (b) in 2 months 4687.25 |реople nonsmokers 1 pack/day or less 2758.5 реople more than 1 pack/day 2553.75 реople (c) in 1 year nonsmokers | рeople 1 pack/day or less people more than 1 pack/day реople
Transcribed Image Text:In a population of 10,000, there are 5000 nonsmokers, 2500 smokers of one pack or less per day, and 2500 smokers of more than one pack per day. During any month, there is an 8% probability that a nonsmoker will begin smoking a pack or less per day, and a 4% probability that a nonsmoker will begin smoking more than a pack per day. For smokers who smoke a pack or less per day, there is a 10% probability of quitting and a 10% probability of increasing to more than a pack per day. For smokers who smoke more than a pack per day, there is a 7% probability of quitting and a 10% probability of dropping to a pack or less per day. How many people will be in each group in 1 month, in 2 months, and in 1 year? (Round your answers to the nearest whole number.) (a) in 1 month nonsmokers 4825 реople 1 pack/day or less 2650 people more than 1 pack/day 2525 people (b) in 2 months 4687.25 |реople nonsmokers 1 pack/day or less 2758.5 реople more than 1 pack/day 2553.75 реople (c) in 1 year nonsmokers | рeople 1 pack/day or less people more than 1 pack/day реople
Expert Solution
Step 1

Consider the provided question,

The transition matrix according to the given data is written as,

  Nonsmokers 1 pack/day or less > 1 pack/day
Nonsmokers 0.88 0.08 0.04
1 pack/day or less 0.1 0.8 0.1
> 1 pack/day 0.07 0.1 0.83

Here, T=0.880.080.040.10.80.10.070.10.83

And the initial vector is X0=0.50.250.25

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