Elementary Statistics (12th Edition)

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

Chapter 4 - Probability - 4-4 Multiplication Rule: Basics - Basic Skills and Concepts - Page 166: 23


0.933, not unlikely.

Work Step by Step

Let A and B be the 2 subjects. Then we have 4 possibilitites: both of them were true positive, bothe of them were true positive, A was true positive, B was true negative and B was true positive, A was true negative .Here the events are dependent, because the sampling was done without replacement. Hence summing the probabilities of the possible cases: $\frac{199}{300} \cdot \frac{118}{299}+\frac{154}{300} \cdot \frac{153}{299}+\frac{154}{300} \cdot \frac{119}{299}+\frac{119}{300} \cdot \frac{154}{299}=0.933.$ Hence it is not unlikely.
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