Question

A​ new, simple test has been developed to detect a particular type of cancer. The test must be evaluated before it is put into use. A medical researcher selects a random sample of 2,000 adults and finds​ (by other​ means) that 4​% have this type of cancer. Each of the 2,000 adults is given the​ test, and it is found that the test indicates cancer in 98​% of those who have it and in 1​% of those who do not.

Answer 1

C = has cancer 
+ = tests positive 

qa 
n(C & +) = 20*.98 = 19.6 ................. n(C & -) = 20 - 19.6 = 0.4 
n(C' & +) = 1980*.02 = 39.6 ............ n(C' & -) = 1980 - 39.6 = 1940.4 

P(C | +) = 19.6/(19.6+39.6) = .3311 
P(C | -) = 0.4/(0.4+1940.4) = .0002061