Bmat question .

Question

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? 

 

 

A 7%

B 25%
C 5%
D 0.7%
E 0.5%

Answer 1

Hello Abi,

A man over 50 has a probability of 1/14 (irrespective of PSA levels) to have prostate cancer.

He also has normal PSA (thus 7/100 of having prostate cancer) and so the probability that he is over 50 and has normal PSA

 is (1/14) x (7/100) = (1/200) = 0.5%.

Hope this helps,

Pradip