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Theoretical Probability versus Experimental Probability

You've heard the terms, theoretical probability and experimental probability, but what do they mean? Are they in anyway related? This is what we are going to discover in this lesson.

If you've completed the lessons on independent and dependent probability, then you've already found the theoretical probability for numerous problems.

Theoretical Probability

Theoretical probability is the probability that is calculated using math formulas. This is the probability based on math theory.

Experimental Probability

Experimental probability is calculated when the actual situation or problem is performed as an experiment. In this case, you would perform the experiment, and use the actual results to determine the probability.

In order to accurately perform an experiment, you must:

  • Identify what constitutes a "trial".

  • Perform a minimum of 25 trials

  • Set up an organizer (table or chart) to record your data.

Let's take a look at an example where we first calculate the theoretical probability, and then perform the experiment to determine the experimental probability. It will be interesting to compare the theoretical probability and the experimental probability. Do you think the two calculations will be close?

Example 1

This problem is from Example 1 in the independent events lesson. We calculated the theoretical probability to be 1/12 or 8.3%. Take a look:

theoretical probability
theoretical probability

Let's take a look at another example where the experimental probability may not be so easy to set-up.

Example 2

theoretical probability
theoretical probability
theoretical probability

I hope this lesson helps you to distinguish between theoretical and experimental probability. Experimental probability can actually be a lot fun!

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