## Odds

Odds are another way of expressing the probability of something happening in the future. Where probability is expressed as the ratio (fraction) of what you are expecting to happen divided by the total number of things that can happen, odds are the ratio (or fraction) of what you are looking for divided by the number of things that you are not looking for.
I will explain this using symbols:

Let     = the number of things (or possibilities) you are looking for

Let     = the number of things (or possibilities) you are not looking for.

Then, the total number of things (or possibilities) is:
+     <=== this is every possibility!
The odds of something happening are
 __
<===what you're looking for divided by
what you are not looking for
The probability of this
same thing happening is
 ____ +
<===what you're looking for divided by the total number of things or possibilities
Here's an example:
What are the odds of drawing a red marble out of a bag
that contains 2 red marbles and 5 blue ones?
Well,
 = 2 red marbles       = 5 blue marbles Then the odds of drawing a red marble is 2 / 5. The probability of drawing a red marble is 2 / (2 + 5) = 2/7