ce cancer is second only to skin in the United States. One of the most common tests for the det is the prostate-specific antigen (PSA) test. However, this test false-positive rate (tests that come back positive for cancer wh ent). Suppose there is a .02 probability that a male patient has resting. The probability of a false-positive test is .75, and thep egative (no indication of cancer when cancer is actually prese: at is the probability that the male patient has prostate cance es back positive? t is the probability that the male patient has prostate cance es back negative? -Ider men, the prior probability of having cancer increases. Supp 3 rother than 02. What is the prob
ce cancer is second only to skin in the United States. One of the most common tests for the det is the prostate-specific antigen (PSA) test. However, this test false-positive rate (tests that come back positive for cancer wh ent). Suppose there is a .02 probability that a male patient has resting. The probability of a false-positive test is .75, and thep egative (no indication of cancer when cancer is actually prese: at is the probability that the male patient has prostate cance es back positive? t is the probability that the male patient has prostate cance es back negative? -Ider men, the prior probability of having cancer increases. Supp 3 rother than 02. What is the prob
Chapter8: Sequences, Series,and Probability
Section8.7: Probability
Problem 11ECP: A manufacturer has determined that a machine averages one faulty unit for every 500 it produces....
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Transcribed Image Text:a monthly payment? Why or why not!
43. Prostate Cancer Screening. According to a 2018 article in Esquire magazine.
Prostate cancer is second only to skin cancer as the most common form of cancor
cancer is the prostate-specific antigen (PSA) test. However, this test is known to hou
a high false-positive rate (tests that come back positive for cancer when no cancer
is present). Suppose there is a .02 probability that a male patient has prostate cancer
before testing. The probability of a false-positive test is .75, and the probability of a
false-negative (no indication of cancer when cancer is actually present) is .20.
a. What is the probability that the male patient has prostate cancer if the PSA test
comes back positive?
b. What is the probability that the male patient has prostate cancer if the PSA test
comes back negative?
c. For older men, the prior probability of having cancer increases. Suppose that the prior
probability of the male patient is .3 rather than .02. What is the probability that the
male patient has prostate cancer if the PSA test comes back positive? What is the prob
ability that the male patient has prostate cancer if the PSA test comes back negative?
d. What can you infer about the PSA test from the results of parts (a), (b), and (c)?
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