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 nonusers 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. (b) In the long term, what proportion of college instructors will be users of this book?

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 nonusers 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. (b) In the long term, what proportion of college instructors will be users of this book?

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Example 3. A preliminary test is customarily given to the students at the beginning of a certain course. The following data are accumulated after several years: (a) 95% of the students pass the course, 5% fail. (b) 96% of the students who pass the course also passed the preliminary test. (c) 25% of the students who fail the course passed the preliminary test. What is the probability that a student who has failed the preliminary test will pass the course? Fail 95% preliminary test pass course 5% fail Figure 3.4 Let A be the event "fails preliminary test" and B be the event “Passes course." The probability we want is then PA(B) in (3.8), so we need P(AB) and P(A). P(AB) is the probability that the student both fails the preliminary test and passes the course; this is P(AB) = (0.95)(0.04) = 0.038. (See Figure 3.4; 95% of the students passed the course and of these 4% had failed the preliminary test.) We also want P(A), the probability that a students fails the preliminary test; this event…
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