Question

College instructors who adopt this book are (we hope) twice as likely to continue to use the book the following year as they are to drop it, whereas non users are seven times as likely to remain nonusers the following year as they are to adopt this book.

(a) Determine the probability that a nonuser will be a user in two years.

Answer 1

The probability that a nonuser of a textbook will become a user in two years is the sum of the probability they remain a nonuser in the first year and become a user in the second, plus the probability they become a user in the first year and remain so.

Step-by-step explanation:

The student is asking about the probability of a nonuser of a textbook becoming a user in two years. Assuming that the probability of a nonuser becoming a user each year is consistent, we’ll use basic probability principles to solve this.

Firstly, we are given that nonusers are seven times as likely to remain nonusers than to become users. Let’s denote the probability of a nonuser becoming a user as p. This means that the probability of remaining a nonuser is 7p. Since these are the only two options, p + 7p = 1, which simplifies to 8p = 1. From here, we can solve for p which is 1/8 or 0.125.

Next, to calculate the probability that a nonuser will be a user in two years, we need to consider two successive probabilities: the probability that they remain a nonuser the first year and then become a user the second year, as well as the probability that they become a user the first year and remain a user the second year.