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 6% 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 1 pack/day or less more than 1 pack/day (b) in 2 months nonsmokers 1 pack/day or less more than 1 pack/day (c) in 1 year nonsmokers 1 pack/day or less 4800 2650 2550 4642 2769 2599 ✔people ✓ people ✔people ✓ people ✔people ✔people people people

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In a population of 10,000, there are 5,000 nonsmokers, 2,500 smokers of one pack or less per day, and 2,500 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 6% 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: 4,800 people
- 1 pack/day or less: 2,650 people
- More than 1 pack/day: 2,550 people

(b) in 2 months:
- Nonsmokers: 4,642 people
- 1 pack/day or less: 2,759 people
- More than 1 pack/day: 2,599 people

(c) in 1 year:
- Nonsmokers: [Box for input]
- 1 pack/day or less: [Box for input]
- More than 1 pack/day: [Box for input]
Transcribed Image Text:In a population of 10,000, there are 5,000 nonsmokers, 2,500 smokers of one pack or less per day, and 2,500 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 6% 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: 4,800 people - 1 pack/day or less: 2,650 people - More than 1 pack/day: 2,550 people (b) in 2 months: - Nonsmokers: 4,642 people - 1 pack/day or less: 2,759 people - More than 1 pack/day: 2,599 people (c) in 1 year: - Nonsmokers: [Box for input] - 1 pack/day or less: [Box for input] - More than 1 pack/day: [Box for input]
Expert Solution
Step 1

The given Information can be depicted as follows:

      During any month  
    Begin smoking 1 pack or less per day Begin smoking more than 1 pack per day Non-smoker
  Non-smoker 8% = 0.08 4% = 0.04 1-0.08-0.04=0.88
At the beginning of a month Smoker who smokes 1 pack or less per day 1-0.10-0.10=0.8 10% = 0.10 10% = 0.10
  Smoker who smokes more than 1 pack per day 10% = 0.10 1-0.10-0.06=0.84 6% = 0.06

 

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