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Q3) A total of 500 married working couples were surveyed whether their annual wages exceeded $ 75,000. The following information was obtained: Wife Less than $ 75,000 More than $ 75,000 Husband Less than $ 75,000 212 36 More than $ 75,000 198 54 a) Assuming that the survey is representative of all married working couples, what is the probability that: 1) Does the husband earn less than $ 75,000? 2) The wife earns more than $ 75,000 or the husband earns more than $ 75,000 3) Does the wife earn more than $ 75,000 given that the husband earn more than $ 75,000? 4) Does the wife earn more than $ 75,000 given that the husband earn less than $ 75,000? 5) Using Bayes' theorem, the probability that the husband earns more than $ 75,000 given that the wife earns more. b) Are the two events independent? Say YES or NO and justify your answer accordingly.

Q3) A total of 500 married working couples were surveyed whether their annual wages exceeded $ 75,000. The following information was obtained: Wife Less than $ 75,000 More than $ 75,000 Husband Less than $ 75,000 212 36 More than $ 75,000 198 54 a) Assuming that the survey is representative of all married working couples, what is the probability that: 1) Does the husband earn less than $ 75,000? 2) The wife earns more than $ 75,000 or the husband earns more than $ 75,000 3) Does the wife earn more than $ 75,000 given that the husband earn more than $ 75,000? 4) Does the wife earn more than $ 75,000 given that the husband earn less than $ 75,000? 5) Using Bayes' theorem, the probability that the husband earns more than $ 75,000 given that the wife earns more. b) Are the two events independent? Say YES or NO and justify your answer accordingly.

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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Q3) A total of 500 married working couples were surveyed whether their annual wages exceeded $ 75,000. The following information was obtained: Husband Wife Less than $ 75,000 More than $ 75,000 Less than $ 75,000 212 198 More than $ 75,000 36 54 a) Assuming that the survey is representative of all married working couples, what is the probability that: 1) Does the husband earn less than $ 75,000? 2) The wife earns more than $ 75,000 or the husband earns more than $ 75,000 3) Does the wife earn more than $ 75,000 given that the husband earn more than $ 75,000? 4) Does the wife earn more than $ 75,000 given that the husband earn less than $ 75,000? 5) Using Bayes' theorem, the probability that the husband earns more than $ 75,000 given that the wife earns more. b) Are the two events independent? Say YES or NO and justify your answer accordingly.
Transcribed Image Text:Q3) A total of 500 married working couples were surveyed whether their annual wages exceeded $ 75,000. The following information was obtained: Husband Wife Less than $ 75,000 More than $ 75,000 Less than $ 75,000 212 198 More than $ 75,000 36 54 a) Assuming that the survey is representative of all married working couples, what is the probability that: 1) Does the husband earn less than $ 75,000? 2) The wife earns more than $ 75,000 or the husband earns more than $ 75,000 3) Does the wife earn more than $ 75,000 given that the husband earn more than $ 75,000? 4) Does the wife earn more than $ 75,000 given that the husband earn less than $ 75,000? 5) Using Bayes' theorem, the probability that the husband earns more than $ 75,000 given that the wife earns more. b) Are the two events independent? Say YES or NO and justify your answer accordingly.
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