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

The following table highlights the difference between Experimental Probability and Theoretical Probability. Scroll down the page for more examples and solutions.

**How to find the Experimental Probability of an event?**
**How to find the Theoretical Probability of an event?**

The Theoretical Probability of an event is the number of ways the event can occur (favorable outcomes) divided by the number of total outcomes.

**What is the Theoretical Probability formula?**

### Experimental Probability

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

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.**How the results of the experimental probability may approach the theoretical probability?**

Example:

The spinner below shows 10 equally sized slices. Heather spun 50 times and got the following results.

a) From Heather's' results, compute the experimental probability of landing on yellow.

b) Assuming that the spinner is fair, compute the theoretical probability of landing in yellow.### Theoretical Probability

### Comparing theoretical and experimental probability

The following video gives an example of theoretical and experimental
probability.

Example:

According to theoretical probability, how many times can we expect to land on each color in a spinner, if we take 16 spins?

Conduct the experiment to get the experimental probability.

We will then compare the Theoretical Probability and the Experimental Probability. The following video shows another example of how to find the theoretical probability of an event.

Examples:

1. A spinner is divided into eight equal sectors, numbered 1 through 8.

a) What is the probability of spinning an odd numbers?

b) What is the probability of spinning a number divisible by 4?

b) What is the probability of spinning a number less than 3?

2. A spinner is divided into eight equal sectors, numbered 1 through 8.

a) What is the probability of spinning a 2?

b) What is the probability of spinning a number from 1 to 4?

b) What is the probability of spinning a number divisible by 2?

The following table highlights the difference between Experimental Probability and Theoretical Probability. Scroll down the page for more examples and solutions.

Step 1: Conduct an experiment and record the number of times the event occurs and the number of times the activity is performed.

Step 2: Divide the two numbers to obtain the Experimental Probability

The Theoretical Probability of an event is the number of ways the event can occur (favorable outcomes) divided by the number of total outcomes.

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 experimental probability of getting a blue marble.

*Solution: *

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

The following video gives another example of experimental probability.

Example:

The spinner below shows 10 equally sized slices. Heather spun 50 times and got the following results.

a) From Heather's' results, compute the experimental probability of landing on yellow.

b) Assuming that the spinner is fair, compute the theoretical probability of landing in yellow.

We can also find the theoretical probability of an event.

*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)Example:

According to theoretical probability, how many times can we expect to land on each color in a spinner, if we take 16 spins?

Conduct the experiment to get the experimental probability.

We will then compare the Theoretical Probability and the Experimental Probability. The following video shows another example of how to find the theoretical probability of an event.

Examples:

1. A spinner is divided into eight equal sectors, numbered 1 through 8.

a) What is the probability of spinning an odd numbers?

b) What is the probability of spinning a number divisible by 4?

b) What is the probability of spinning a number less than 3?

2. A spinner is divided into eight equal sectors, numbered 1 through 8.

a) What is the probability of spinning a 2?

b) What is the probability of spinning a number from 1 to 4?

b) What is the probability of spinning a number divisible by 2?

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