What Is Probability?

I am sure most of you all have at least heard of probability and know what it is.  If you have ever flipped a coin that is fair, you already know that the probability of getting heads is 1/2.  In general, probability theory is the area of mathematics that deals with reasoning about uncertainty.

The notation for probability in this wiki will be $Pr(event)$.  For example, $Pr(coin flip = heads) = 0.5$, which means the probability of a coin flip ending up as heads is 0.5.  I may also notate that event as $Pr(heads) = 0.5$. Note that in some texts, you may see $P(event)$ instead of $Pr(event)$.  

Probability in mathematics and statistics has a precise definition and must be between 0 and 1.

$0 \leq Pr(event) \leq 1$

Additional properties of probabilities are explained on the following page.  To enhance your understanding, you may want to view our page on Set Theory, which explains much of the terminology you will see.