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

Multiple-choice exercise

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Box I contains 5 red and 3 white balls. Box II contains 4 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?

61%

31.3%

51.3%

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 95% accurate, which we'll say means that if a person is a drug user, the result is positive 95% of the time, and if the person is not a drug user, the result is negative 95% 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.)

50%

95%

9.5%

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 30% 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 95% accuracy giving a positive result 95% of the time for people who are drug users and a negative result 95% 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?

89.1%

95%

32%

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

A manufacturer obtains computer modems from three different subcontractors: 25% from A, 40% from B, and 35% 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?

54.9%

1.4%

4%

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