# Theoretical Probability and Experimental Probability

The probability of an event is a number from 0 to 1 that measures
the chance that an event will occur. In these lessons, we will look
into experimental probability and theoretical probability.

Related Topics:

More Probability Lessons

## Experimental Probability

One way to find the probability of an event is to conduct an
experiment.

*Example: *

A bag contains 10 red marbles, 8 blue marbles and 2 yellow
marbles. Find the experimental probability of getting a blue
marble.

*Solution: *

Take a marble from the bag.

Record the color and return the marble.

Repeat a few times (maybe 10 times).

Count the number of times a blue marble was picked (Suppose it is
6).

The experimental probability of getting a blue marble from the
bag is

How to find and use experimental probability. The following
video gives another example of experimental probability.

The following video illustrates how the results of the
experimental probability may approach the theoretical probability.

## Theoretical Probability

We can also find the theoretical probability of an event.

The formula for theoretical probability of an event is

*Example: *

A bag contains 10 red marbles, 8 blue marbles and 2 yellow
marbles. Find the theoretical probability of getting a blue
marble.

*Solution: *

There are 8 blue marbles. Therefore, the number of favorable
outcomes = 8.

There are a total of 20 marbles. Therefore, the number of total
outcomes = 20

*Example: *

Find the probability of rolling an even number when you roll a
die containing the numbers 1-6. Express the probability as a
fraction, decimal, ratio and percent.

*Solution: *

The possible even numbers are 2, 4, 6. Number of favorable
outcomes = 3.

Total number of outcomes = 6

The probability = (fraction) = 0.5 (decimal) = 1:2 (ratio)
= 50% (percent)

#### Comparing theoretical and experimental probability

The following video gives another example of theoretical
probability.

The following video shows another example of how to find the
theoretical probability of an event.