APFIVE Bayes Theorem And Medical Testing
I.
The probability that a person with the disease tests positive is $$0.90$$.
II.
The probability that a person without the disease tests positive is $$0.05$$.
III.
By applying Bayes’ Theorem, the probability that a person who tests positive actually has the disease is given by $$\frac{0.05 \times 0.05}{0.05 \times 0.05 + 0.95 \times 0.90}$$, which is approximately 0.0029.
Which of the above statements is/are true?
Disease Testing Scenario:
| Condition | Disease Present | Disease Absent |
|---|---|---|
| Test Positive | 0.90 | 0.05 |
| Test Negative | 0.10 | 0.95 |
Overall, 5% of the population has the disease.
A
I, II, and III
B
I only
C
II only
D
I and II only
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