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Experimental and Theoretical Probabilities

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Probability Calculations

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Experimental and Theoretical Probabilities

Geometry

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It is discovered that the experimental probability of an event approaches the theoretical probability as the number of trials increases.

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Now You Know

After completing this tutorial, you will be able to complete the following:

  • List the theoretical probability of the outcomes of a simple probability experiment.
  • Compare the results of an experiment to the theoretical probability.
  • Recognize that the experimental probability of an event approaches the theoretical probability as the number of trials increases.

Everything You'll Have Covered

Theoretical probability is calculated by dividing the number of outcomes for a specific event by the number of total events possible.

For example, when flipping a penny, the penny could land on either heads or tails resulting in two possible outcomes. To determine the probability of the penny landing on heads:

In this Activity Object, students will use several events to calculate a specific outcome such as a spinner, a toy coin, and a deck of cards. The theoretical probability is referred to as the "Estimated Probabilities."

Experimental probability is the ratio of the number of times the event actually occurs to the total number of trials.

For example, if we flip a penny 30 times, we would expect that the coin would land on heads 15 out of 30 times. However, when the experiment is conducted is it possible that the coins will land on heads more or less frequently since the process of flipping a coin is random.

The more trials performed in a probability experiment, the more similar the experimental and theoretical probabilities become. In the table below, you can observe that as the number of trials increased, the experimental probabilities approached the theoretical probabilities.

is just one-fiftieth below , which is equal to .

is just one-fiftieth above , which is equal to .

In this Activity Object, students can increase the trials to observe how the experimental probability becomes closer to the theoretical probability.

Tutorial Details

Approximate Time 15 Minutes
Pre-requisite Concepts Students should know the concept of theoretical probability.
Course Geometry
Type of Tutorial Concept Development
Key Vocabulary experimental probability, outcome, theoretical probability