MA/STAT416: ProbabilityLecture NotesSpring 20111Chapter 3: Conditional Probability and IndependenceFebruary 9, 20113.4More on Bayes’ Theorem1.Blood Tests.A certain blood test for a disease gives a positive result 90% of thetimes among patients having the disease. But it also gives a positive result 25% ofthe times amon people who do not have the disease. It is believed that 30% of thepopulation has this disease. What is the probability that a person with a positivetest result indeed has the disease?2.Politics.75% of Democrats and 25% of Republicans are pro-choice.In thepopulation, 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 examhave 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 sherandomly picks one of the five alternatives as her choice.Suppose a particularproblem was answered correctly.
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