Approximately 1 in 14 men over the age of 50 has prostate cancer. The level of ‘prostate specific antigen’ (PSA) is used as a preliminary screening test for prostate cancer.

7% of men with prostate cancer do not have a high level of PSA. These results are known as ‘false negatives’.

75% of those men with a high level of PSA do not have cancer. These results are known as ‘false positives’.

If a man over 50 has a normal level of PSA, what are the chances that he has prostate cancer?

Two things we cannot get confused in this question is the probability of this man getting Prostate cancer, and if he is a man that has prostate cancer.

We first speak of the scenario that he gets prostate cancer. This is adding two possibilities together; first that he is of the 7% that have “false negatives” and second that he then becomes 1/14 of those who now have prostate cancer.

The total permuation becomes: \frac{7}{100} + \frac{1}{14} = \frac{99}{700}= 0.14

Notice the question says "7% of men with prostate cancer do not have a high level of PSA ", and we know that 1/14 men have prostate cancer means that the probability is actually 7% OF the 1/14.

Finally we can say the total possibility of one man that has normal PSA levels having cancer, is 0.14 x 0.005 which is 0.0007 and that makes up in percentage; 0.7% and our answer is D.

Hello!
I am bringing this up again.
If 7% out of men with prostate cancer do not have a high level of PSA then why is the first calculation needed?
It seems to me that 0.07 x 1/14 = 0.005 must be the answer. Hence answer E should be the right one. Can anyone please go over the question and explain me?