Elementary Statistics (12th Edition)

Published by Pearson
ISBN 10: 0321836960
ISBN 13: 978-0-32183-696-0

Chapter 4 - Probability - Review - From Data To Decision - Page 192: 9


Not the same.

Work Step by Step

We know that $probability=\frac{number \ of \ good \ outcomes}{number\ of\ all\ outcomes}$. We first consider the probability that a subject is infected given a positive test result. Hence here $probability=\frac{17}{17+2}=0.895.$ We now find the inverse, which is the probability that there is a positive test result given that the subject is infected: Hence here $probability=\frac{17}{17+6}=0.739.$ Hence we can see that the statement and the inverse are not equal, reflecting the confusion of the inverse.
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