A population of 10000 is grouped as follows 5000 nonsmokers

A population of 10,000 is grouped as follows: 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 a 7% probability that a nonsmoker will begin smoking a pack or less per day, and a 3% 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 and in 2 months? (Round your answers to the nearest whole number.)

(a) in 1 month

(b) in 2 months

Solution

a)

number of non smokers in 1 month

= 5000 - (7% + 3%) * 5000 + 10% * 2500 + 7% * 2500

= 4925

number of 1pack/day or less

= 2500 - (10% +10%) * 2500 + 7% * 5000 + 10% * 2500

= 2600

number of smokers who smoke more than 1 pack/day

= 10000 - 4925 - 2600

= 2475

b)

number of non smokers in 2 month

= 4925 - (7% + 3%) * 4925 + 10% * 2600 + 7% * 2475

= 4866

number of 1pack/day or less

= 2600 - (10% +10%) * 2600 + 7% * 4925 + 10% * 2475

= 2672

number of smokers who smoke more than 1 pack/day

= 10000 - 4866 - 2672

= 2462