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Consider a population with the following properties. i. No one in the population is both old and skeptical. 45 ii. of the population is old. 82 iii. Of those who are old, å are smiling. iv. Of those who are not old, are smiling. v. H of the population is skeptical. vi. Of those who are skeptical, are smiling. vii. Of those who are not skeptical, are smiling. Use this information to explain why everyone in the population who is smiling must be either old or skeptical.

Consider a population with the following properties. i. No one in the population is both old and skeptical. 45 ii. of the population is old. 82 iii. Of those who are old, å are smiling. iv. Of those who are not old, are smiling. v. H of the population is skeptical. vi. Of those who are skeptical, are smiling. vii. Of those who are not skeptical, are smiling. Use this information to explain why everyone in the population who is smiling must be either old or skeptical.

A First Course in Probability (10th Edition)
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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Consider a population with the following properties. i. No one in the population is both old and skeptical. ii. 5 of the population is old. iii. Of those who are old, a are smiling. iv. Of those who are not old, are smiling. H of the population is skeptical. V. vi. Of those who are skeptical, are smiling. vii. Of those who are not skeptical, are smiling. Use this information to explain why everyone in the population who is smiling must be either old or skeptical. (Hint: use Bayes' rule to separately calculate the probabilities that someone is old or skeptical given that they are smiling.)
Transcribed Image Text:Consider a population with the following properties. i. No one in the population is both old and skeptical. ii. 5 of the population is old. iii. Of those who are old, a are smiling. iv. Of those who are not old, are smiling. H of the population is skeptical. V. vi. Of those who are skeptical, are smiling. vii. Of those who are not skeptical, are smiling. Use this information to explain why everyone in the population who is smiling must be either old or skeptical. (Hint: use Bayes' rule to separately calculate the probabilities that someone is old or skeptical given that they are smiling.)
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