Practice Quiz - Section 7-4 (Form B) - Bayes' Formula

Multiple-choice exercise

Work out the problem on paper and then choose the letter for your answer. After you have successfully answered all questions, look at the top of the page to see how you did.

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Box I contains 7 red and 3 white balls. Box II contains 2 red and 6 white balls. First a box is selected at random (each box is as likely to be selected as the other) and then a ball is drawn from the box. If a red ball is drawn, what is the probability that it came from Box I?

73.7%

35%

47.5%

None of the answers given; click to see the solution.

Probability can be used to interpret the results of a test given to determine if a person is using drugs. Suppose we assume that 5% of people are drug users. A test is 96% accurate, which we'll say means that if a person is a drug user, the result is positive 96% of the time, and if the person is not a drug user, the result is negative 96% of the time. A randomly chosen person tests positive. What is the probability that the person is a drug user? (This question is based on a discussion which appeared in the column "Ask Marilyn" in Parade Magazine on March 28, 1993.)

55.8%

96%

8.6%

None of the answers given; click to see the solution.

Suppose that the test for drug use in question #2 is given to a group of people who are known to have a higher likelihood of being drug users. Assume 40% of the people in this group are drug users. Using a test with the same accuracy as in question #2 (that is, a test with 96% accuracy giving a positive result 96% of the time for people who are drug users and a negative result 96% of the time for people who are not drug users), what is the probability that an individual in this group who tests positive really is a drug user?

94.1%

96%

40.8%

None of the answers given; click to see the solution.

A manufacturer obtains computer modems from three different subcontractors: 30% from A, 45% from B, and 25% from C. Past experience has shown that the defective rates for these subcontractors are 3%, 1%, and 4% respectively. If a modem is returned to the manufacturer by a customer because it was found to be defective, what is the probability that it came from subcontractor C?

42.6%

1%

4%

None of the answers given; click to see the solution.