A funny example from probability calculus:

Consider a set of 100000 women, all of which are regularly taking the birth control pill (probability of success: 99.99%). Furthermore, they all do a pregnancy test (probability of success: 99.99%).

What is the probability that given a positive test result, this actually implies a pregnancy?

Here's the calculation:

100000 * 0.0001 = 10 women will get pregnant despite taking the pill and hence get a positive test result

(the pill fails with probability 0.01%).

100000 * 0.0001 = 10 women will get a positive test result, although they are not pregnant

(the test fails with probability 0.01%)

So, out of 20 positive test results, only 10 women are actually pregnant. Thus, the probability that a positive test result implies a pregnancy is 50%.

What does that tell you?

Greets,

Philip