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Lecture5_print - MA/STAT416 Probability Lecture Notes...

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MA/STAT416: Probability Lecture Notes Spring 2011 1 Chapter 3: Conditional Probability and Independence February 9, 2011 3.4 More on Bayes’ Theorem 1. Blood Tests. A certain blood test for a disease gives a positive result 90% of the times among patients having the disease. But it also gives a positive result 25% of the times amon people who do not have the disease. It is believed that 30% of the population has this disease. What is the probability that a person with a positive test result indeed has the disease? 2. Politics. 75% of Democrats and 25% of Republicans are pro-choice. In the population, 48% are Democrats and 52% are Republicans. If Cathy is pro-life, what is the probability that she is a Republican? 3. Multiple Choice Tests. Suppose that the questions in a multiple choice exam have five alternatives each, of which a student picks one as the correct alternative. A student either knows the truly correct alternative with probability 0.7, or she randomly picks one of the five alternatives as her choice. Suppose a particular problem was answered correctly.
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