Question

An athlete suspected of having used steroids is given two tests that operate independently of each other. test a has probability 0.92 of being positive if steroids have been used. test b has probability 0.7 of being positive if steroids have been used. what is the probability that neither test is positive if steroids have been used?

Answer 1

There is a 2.4% chance of getting two negative tests.

The chance the first test is positive is 0.92, therefore the chance it is negative is 0.08.

The chance the second test is positive is 0.3, therefore the chance is it negative is 0.3.

To find the chance that both tests are negative, we have to multiply them together.

0.08 x 0.3 = 0.024 = 2.4%