Bayes Theorem And Medical Testing

Question

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 $$\frac{0.05 	imes 0.05}{0.05 	imes 0.05 + 0.95 	imes 0.90} \approx 0.0029$$.

Which of the statements is/are true?

Accepted Answer

I and II only

Answer

I only

Answer

I, II, and III

Answer

II only

Rank	User	Correct Count	Attempt Count	Total Time	Score
#1	minapup17	1	1	0m 00s	100
#2	halllais304	1	1	1m 05s	35
#3	abygail.gonzalez69	1	2	1m 32s	-2
#4	2822714282	0	2	0m 00s	-20

Bayes Theorem And Medical Testing

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