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What is Theoretical Probability? – Definition, Formula & Examples

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Have you ever heard someone ask, ‘What are the odds?’ Usually what it is meant is, ‘How likely is it that an event will happen?’ This lesson explores finding the likelihood, or theoretical probability, that an event could occur.
Coin Toss Probability
Coin toss, heads or tails?
Coin Toss ClipArt
The very first Super Bowl was played at Anaheim Stadium in Los Angeles in 1967. It was a battle between the Green Bay Packers and the Kansas City Chiefs. This historical game started the same way all football games begin, with a coin toss. If you were standing on the 50-yard line as one of the team captains, what are the odds that you would win the coin toss? If you said 50% you were right. Here’s how it’s calculated…

A normal coin has two sides, heads and tails. So, when you flip a coin, there are two, and only two, possible outcomes; the coin either lands with the head side up or it lands with the tails side up. So, the total number of possible outcomes for a coin flip is 2, and it is equally likely for the coin to land on either side. This means the probability of getting heads (or tails) on a single flip of the coin is 1 out of 2, or 50%.

Probability of an Event
But what if the odds are not as even as 50/50? Well, let’s suppose there were a gumball machine filled with red, green, yellow, orange and blue gumballs, and you only had one quarter to get a red one. In order to calculate the probability, you need to know two things: (a) the total number of gumballs in the machine, and (b) the number of red ones.

Definition of Theoretical Probability
Definition of Probability
The total number of gumballs represents the total possible outcomes, supposing that you are equally likely to pick any one of them. And the number of red gumballs represents the number of possible favorable outcomes (outcomes you are interested in). So, the theoretical probability is equal to the number of favorable outcomes (in this case the number of red gumballs) divided by the total number of possible outcomes (in this case the total number of gumballs in the machine).

Examples
Example A:

Gumball machine
Gum Ball Machine http://www.okmfg.net/history-of-gumball-machine.html
There are 5 red balls, 7 green balls and 13 blue balls in the bag.

 
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