Officials at the suicide prevention center know that 5% of all people who phone their hotline actually attempt suicide. A psychologist has devised a quick and simple verbal test to help identify those callers who will actually attempt suicide. She found that a. 80% of the people who will attempt suicide have a positive score on this test; b. but only 5% of those who will not attempt suicide have a positive score on this test. If you get a positive identification from a caller on this test, what is the probability that he would actually attempt suicide?

A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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Officials at the suicide prevention center know that 5% of all people who phone their hotline actually
attempt suicide. A psychologist has devised a quick and simple verbal test to help identify those callers
who will actually attempt suicide. She found that
a. 80% of the people who will attempt suicide have a positive score on this test;
b. but only 5% of those who will not attempt suicide have a positive score on this test.
If you get a positive identification from a caller on this test, what is the probability that he
would actually attempt suicide?
Many diagnostic tests for detecting diseases do not test for the disease directly but for a chemical or
biological product of the disease, hence are not perfectly reliable. The sensitivity of a test is the
probability that the test will be positive when administered to a person who has the disease. The higher
the sensitivity, the greater the detection rate and the lower the false negative rate. Suppose the
sensitivity of a diagnostic procedure to test whether a person has a particular disease is 85%. A person
who actually has the disease is tested for it using this procedure by two independent laboratories.
• The probability that both test results will be positive is
The probability that at least one of the two test results will be positive
Transcribed Image Text:Officials at the suicide prevention center know that 5% of all people who phone their hotline actually attempt suicide. A psychologist has devised a quick and simple verbal test to help identify those callers who will actually attempt suicide. She found that a. 80% of the people who will attempt suicide have a positive score on this test; b. but only 5% of those who will not attempt suicide have a positive score on this test. If you get a positive identification from a caller on this test, what is the probability that he would actually attempt suicide? Many diagnostic tests for detecting diseases do not test for the disease directly but for a chemical or biological product of the disease, hence are not perfectly reliable. The sensitivity of a test is the probability that the test will be positive when administered to a person who has the disease. The higher the sensitivity, the greater the detection rate and the lower the false negative rate. Suppose the sensitivity of a diagnostic procedure to test whether a person has a particular disease is 85%. A person who actually has the disease is tested for it using this procedure by two independent laboratories. • The probability that both test results will be positive is The probability that at least one of the two test results will be positive
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