# Counting and Probability

## What is Probability?

Simply put, probability is the chance of something happening. It is the comparison of the number of times an event could occur to the total number of possible events. People use probability all the time, from meteorologists predicting the weather, to researchers conducting surveys, average people talking about their routines, and even when someone wins the lottery!

## So what does counting have to do with this?

We know that counting is the action of finding the number of elements of a finite of objects. To find a probability, we need to count the number of times an event could occur and also the total number of possible events. If these numbers are large,we need efficient ways of counting to handle the data and better understand it.

## How can we count the number of possible outcomes?

• The number of possible outcomes for an event E is n(E).
• If there are two or more mutually exclusive events (there are no common outcomes) then the total number of possible outcomes is the sum of the outcomes of the mutually exclusive events. For example, the possibility of rolling 1 or 6 on a dice is n(1)+n(6)
• If two or more events have common outcomes, then the total number of possible outcomes is their product. For example, if we have 4 shirts and 2 pants the number of possible outfits is 4x2=8.

For clarification, visit this helpful page:

## What are my chances of winning the lottery?

You'd be more likely to get struck by lightning twice in your life!
Mega Millions Jackpot Probability