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
Chapter8: Sequences, Series,and Probability
Section8.7: Probability
Problem 4ECP: Show that the probability of drawing a club at random from a standard deck of 52 playing cards is...
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Note:- Please need all the answers for Part a, b, c with a full explanation for this problem.
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,
And the initial vector is
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