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.

Question

Mathematics

Pranav Goodwin

23 June, 19:02

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.

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Cobweb · 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