A population of 100,000 consumers is grouped as follows: 20,000 users of Brand A, 30,000 users of Brand B, and 50,000 who use neither brand. During any month a Brand A user has a 20% probability of switching to Brand B and a 10% probability of not using either brand. A Brand B user has a 15% probability of switching to Brand A and a 20% probability of not using either brand. A nonuser has a 20% probability of purchasing Brand A and a 25% probability of purchasing Brand B. How many people will be in each group in 1 month?
A) The number of people in each group is as follows: 30,300 users of Brand A, 36,000 users of Brand B, and 33,700 who use neither brand.
B) The number of people in each group is as follows: 41,700 users of Brand A, 28,500 users of Brand B, and 29,800 who use neither brand.
C) The number of people in each group is as follows: 35,500 users of Brand A, 30,300 users of Brand B, and 34,200 who use neither brand.?
D) The number of people in each group is as follows: 28,500 users of Brand A, 36,000 users of Brand B, and 35,500 who use neither brand.
E) The number of people in each group is as follows: 30,300 users of Brand A, 41,700 users of Brand B, and 28,000 who use neither brand.

Question

Quizplus · Accepted Answer

To find the number of people in each group after 1 month, we calculate the transitions based on the given probabilities. Starting with 20,000 Brand A users, 30,000 Brand B users, and 50,000 nonusers:- From Brand A to Brand B: 20,000 * 20% = 4,000- From Brand A to nonusers: 20,000 * 10% = 2,000- Remaining Brand A users: 20,000 - 4,000 - 2,000 = 14,000- From Brand B to Brand A: 30,000 * 15% = 4,500- From Brand B to nonusers: 30,000 * 20% = 6,000- Remaining Brand B users: 30,000 - 4,500 - 6,000 = 19,500- From nonusers to Brand A: 50,000 * 20% = 10,000- From nonusers to Brand B: 50,000 * 25% = 12,500- Remaining nonusers: 50,000 - 10,000 - 12,500 = 27,500Adding the transitions to the remaining users:- New Brand A users: 14,000 (remaining) + 4,500 (from Brand B) + 10,000 (from nonusers) = 28,500- New Brand B users: 19,500 (remaining) + 4,000 (from Brand A) + 12,500 (from nonusers) = 36,000- New nonusers: 27,500 (remaining) + 2,000 (from Brand A) + 6,000 (from Brand B) = 35,500

A Population of 100,000 Consumers Is Grouped as Follows: 20,000