Question

A blood test to detect prostate cancer in men gives a positive result 96% of the time if a person has prostate cancer, and it is 97% accurate for people who do not have the disease. What is the probability of getting a false positive result (that is, a person tests positive but does not actually have the ailment)?

A.
0.01
B.
0.03
C.
0.04
D.
0.07
E.
0.97

Answer 1

Edit: The previous answer was wrong, sorry! The correct answer is B. 0.03. I included a handy chart to help you. By plugging in the information, such as that 96% was accurate for those who did have cancer, and was 97% accurate to tell that a person does not have cancer, I was able to find both the False Negative and the False Positive.

Answer 2

Answer: Option 'B' is correct.

Explanation:

Since we have given that

Probability that a blood test gives a positive result if a person has prostate cancer = 96%

Probability that a blood test is accurate for people who do not have the disease P(A) = 97%

We need to find the probability of getting a false positive result i.e. a person tests positive but does not actually having the ailment.

So, our required probability would be

`P(A')=1-P(A)\\\\P(A')=1-0.97\\\\P(A')=0.03`

Hence, Option 'B' is correct.