Question

Consider the following statement about the practice of "doping" (using prohibited performance-enhancing drugs) in professional sports:

-20% of negative doping tests prove to be incorrect.

Explain how this is different from the statement,

-20% of athletes who dope will test negative.

Answer 1

Let D denote the event that s randomly selected athlete dopes

and C denote the event that the test result is correct

The event that negative doping test is incorrect is (C' given D')

The event that athlete who dope will test negative is (C' given D)

Thus, P(C' | D') = 0.20 and also P(C' | D) = 0.20