Theoretical Probability and Experimental Probability

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)

The following video gives another example of theoretical probability.

Comparing theoretical and experimental probability.

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