Theoretical vs Experimental Probability Explained

This lesson explains the difference between theoretical and experimental probability. Theoretical probability is based on expected outcomes, while experimental probability is based on actual results. Through examples involving a spinner and dice, the lesson demonstrates how these probabilities can differ and converge with more trials. It also shows how probability can be used to make predictions, such as estimating future DVD sales based on past data. The lesson concludes with a summary and a motivational message from the Math Fun Academy.

What is theoretical probability based on?

• Definitions and principles learned in previous lessons

• Random guesses

• Predictions made without conducting an experiment

• Actual outcomes of an experiment

What is experimental probability?

• A fixed value for all experiments

• A theoretical calculation

• What actually occurs during an experiment

• A prediction of an outcome

What was the experimental probability of landing on red in the spinner experiment?

• 0.6

• 0.5

• 0.4

• 0.3

As the number of attempts in an experiment increases, what is expected to happen to the theoretical and experimental probabilities?

• They become less similar

• They become unpredictable

• They become more similar

• They remain constant

Why might theoretical and experimental probabilities not always match?

• Theoretical probability is always incorrect

• Because of insufficient trials

• Due to experimental error

• Experimental probability doesn't exist

In the dice experiment, what was the theoretical probability of rolling a sum of nine?

• 2/5

• 1/9

• 1/6

• 4/36

What could be a reason for the discrepancy between theoretical and experimental probabilities in the dice experiment?

• All outcomes are equally likely

• Faulty dice

• Not enough trials

• Incorrect calculations

How can theoretical and experimental probability be used?

• To make predictions about future events

• To guarantee outcomes in experiments

• To prove that theoretical probability is always accurate

• To change the results of past experiments

What was the probability of a customer buying a comedy DVD based on last year's sales?

• 58%

• 20%

• 50%

• 29%

How many comedies should the store owner buy this year assuming the trend continues?

• 500

• 145

• 2900

• 1450