Question

Suppose that 5% of athletes at a certain university are using steroids or other

performance-enhancing drugs (PEDs). Unfortunately, the tests used to detect PEDs
aren't perfect. Suppose that 3% of athletes who are not using PEDs will test positive
and be accused of using PEDs. Meanwhile, 1% of athletes who are using PEDs will test
negative and escape detection. Calculate the probability that a randomly selected
athlete will test positive.

Answer 1

There is a 8.11% of any randomly selected athlete to test positive.

Explanation:

To make it easier, let's assume there are 100 athletes

5/100 have it

3/95 do not have it, but will test positive

1% of the 5 athletes who are using PEDs = 0.05%

This means that 4.95/100 will test positive

3/95 = 3.16%

(rounded, if you need a more precise answer, it's 3.1578947368421053)

3.16% + 4.95% = 8.11%