What Is Conditional Probability?

$$\text{The Sickening}$$

=== The World Health Organization has just identified a new disease. The good news is that it is very rare: only $1$ in every million people has it. The bad news is that it is very deadly.

There is a test available that can tell you whether or not you have the disease. It gives the correct diagnosis $99$% of the time. This means that if someone with the disease is tested, the test will say "positive" $99$% of the time and "negative" $1$% of the time; if someone without the disease is tested, it will say "negative" $99$% of the time and "positive" $1$% of the time.