Probability

The probability of an event represents the frequency, or chance, that the event will happen.

For notation, if A is an event, P(A) is the probability of the occurrence of the event.

We can define the actual probability of an event, A, as follows:

Here, A is the event in question. Think of an entire universe of events where anything is possible, and let's represent it as a circle. We can think of a single event, A, as being a smaller circle within that larger universe, as shown in the following diagram:

Let's now pretend that our universe involves a research study on humans, and the A event is people in that study who have cancer.

If our study has 100 people and A has 25 people, the probability of A or P(A) is 25/100.

The maximum probability of any event is 1. This can be understood as the red circle grows so large that it is the size of the universe (the larger circle).

The most basic examples (I promise they will get more interesting) are coin flips. Let's say we have...