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1) A bin is filled with half red balls and half purple balls. Approximately 20% of the red balls have a stripe on them, and the others do not. Approximately 90% of the purple balls have a stripe on them and the others do not. A ball is randomly selected, and it is striped. What is the probability it is purple? (Hint: Draw a tree diagram)
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2) Suppose that the reliability of a test for hepatitis is specified as follows: Of people with hepatitis, 95% have a positive reaction and 5% have a negative reaction; of people free of hepatitis, 90% have a negative reaction. From a large population of which .05% of the people have hepatitis, a person is selected at random and given the test. If the test is negative, what is the probability that the person actually has hepatitis?
3) Use Bayes theorem. There are three sections of English 101. In section I there are 25 students, of whom 5 are mathematics majors. In section II there are 20 students, of whom 6 are mathematics majors. In section III there are 35 students, of whom 5 are mathematics majors. A student in English 101 is randomly selected. Find the probability that the student is from section I, given that he or she is a mathematics major.
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