APFIVE Bayes Theorem And Medical Testing
Five percent of a population has a certain disease. A diagnostic test for the disease provides the results shown in the table, which lists the conditional probabilities of a test result given the patient’s disease status.
| Test Result | Disease Present | Disease Absent |
|---|---|---|
| Test Positive | 0.90 | 0.05 |
| Test Negative | 0.10 | 0.95 |
Consider the following statements:
I. The probability that an individual with the disease will test positive is $$0.90$$.
II. The probability that an individual without the disease will test positive is $$0.05$$.
III. The probability that an individual who tests positive actually has the disease is $$\frac{0.05 \times 0.05}{0.05 \times 0.05 + 0.95 \times 0.90} \approx 0.0029$$.
Which of the statements is/are true?
A
I and II only
B
I, II, and III
C
I only
D
II only
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