85% of the restaurants in Camden Town practice good hygiene. Each time you eat in a clean restaurant, there is a 4% chance that you will get sick, independent of your previous visits. Each time you eat in a restaurant that does not practice good hygiene, on the other hand, there is a 40% chance that you will get sick, independent of your previous visits. 1. You eat at a restaurant in Camden Town and you get sick. What is the probability that the restaurant practices good hygiene? Hint: Using the law of total probability, first calculate the probability of the event ‘falling sick’. You can use this probability in your subsequent application of Bayes’ Theorem. 2. You go to the same restaurant for a second time, and you get sick again. What is the probability of the restaurant practicing good hygiene now? Hint: Using the law of total probability, first calculate the probability of the event ‘falling sick twice’. In this calculation, you can use the conditional independences P(falling sick twice|restaurant clean) = P(falling sick once|restaurant clean)2 and P(falling sick twice|restaurant not clean) = P(falling sick once|restaurant not clean)2. You can use these probabilities in your subsequent application of Bayes’ Theorem, where you can again use the same conditional independence.

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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85% of the restaurants in Camden Town practice good hygiene. Each time you eat in a clean restaurant, there is a 4% chance that you will get sick, independent of your previous visits. Each time you eat in a restaurant that does not practice good hygiene, on the other hand, there is a 40% chance that you will get sick, independent of your previous visits. 1. You eat at a restaurant in Camden Town and you get sick. What is the probability that the restaurant practices good hygiene? Hint: Using the law of total probability, first calculate the probability of the event ‘falling sick’. You can use this probability in your subsequent application of Bayes’ Theorem. 2. You go to the same restaurant for a second time, and you get sick again. What is the probability of the restaurant practicing good hygiene now? Hint: Using the law of total probability, first calculate the probability of the event ‘falling sick twice’. In this calculation, you can use the conditional independences P(falling sick twice|restaurant clean) = P(falling sick once|restaurant clean)2 and P(falling sick twice|restaurant not clean) = P(falling sick once|restaurant not clean)2. You can use these probabilities in your subsequent application of Bayes’ Theorem, where you can again use the same conditional independence.

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