A population of 10,000 is grouped as follows: 5,000 nonsmokers, 3,500 smokers of one pack or less per day, and 1,500 smokers of more than one pack per day. During any month there is a 5% 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 5% probability of quitting and a 20% probability of dropping to a pack or less per day. How many people will be in each of the three groups in 1 month?
A) The number of people in each group is as follows: 5,475 nonsmokers, 3,150 smokers of one pack or less per day, and 1,375 smokers of more than one pack per day.
B) The number of people in each group is as follows: 4,975 nonsmokers, 3,350 smokers of one pack or less per day, and 1,675 smokers of more than one pack per day.
C) The number of people in each group is as follows: 5,475 nonsmokers, 3,350 smokers of one pack or less per day, and 1,175 mokers of more than one pack per day.
D) The number of people in each group is as follows: 4,975 nonsmokers, 3,150 smokers of one pack or less per day, and 1,875 mokers of more than one pack per day.
E) The number of people in each group is as follows: 4,775 nonsmokers, 1,875 smokers of one pack or less per day, and 3,350 smokers of more than one pack per day.

Question

Quizplus · Accepted Answer

To calculate the number of people in each group after one month, we need to apply the given probabilities to the initial populations:1. Nonsmokers (initially 5,000):- 5% become smokers of one pack or less: 5,000 * 0.05 = 250- 4% become smokers of more than one pack: 5,000 * 0.04 = 200- Remaining nonsmokers: 5,000 - 250 - 200 = 4,5502. Smokers of one pack or less (initially 3,500):- 10% quit: 3,500 * 0.10 = 350- 10% increase to more than one pack: 3,500 * 0.10 = 350- New smokers from nonsmokers: 250- Remaining in this group: 3,500 - 350 - 350 + 250 = 3,050- However, we also need to add those who drop from more than one pack per day to one pack or less, which is 20% of 1,500 = 300- So, the adjusted total is 3,050 + 300 = 3,3503. Smokers of more than one pack (initially 1,500):- 5% quit: 1,500 * 0.05 = 75- 20% drop to one pack or less: 1,500 * 0.20 = 300- New smokers from nonsmokers: 200- Remaining in this group: 1,500 - 75 - 300 + 200 = 1,325- However, we also need to add those who increase from one pack or less to more than one pack, which is 10% of 3,500 = 350- So, the adjusted total is 1,325 + 350 = 1,675Therefore, after one month, there will be 4,550 nonsmokers, 3,350 smokers of one pack or less per day, and 1,675 smokers of more than one pack per day.

A Population of 10,000 Is Grouped as Follows: 5,000 Nonsmokers