Experimental and Theoretical Probability

This lesson covers the difference between experimental (empirical) probability and theoretical probability, as required by the AQA GCSE Mathematics specification. You will learn how to estimate probabilities from experiments, understand relative frequency, and determine whether an object (such as a die or spinner) is fair or biased.

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Theoretical Probability

Theoretical probability is calculated by reasoning about equally likely outcomes, without carrying out an experiment.

P(event) = number of favourable outcomes / total number of equally likely outcomes

For example, the theoretical probability of rolling a 3 on a fair die is 1/6, because there are 6 equally likely outcomes and exactly one of them is a 3.

Theoretical probability assumes that the situation is fair (unbiased). If a coin is fair, P(heads) = 1/2 exactly.

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Experimental Probability (Relative Frequency)

Experimental probability (also called relative frequency) is calculated from the results of an actual experiment or from observed data.

Relative frequency = number of times the event occurred / total number of trials

Worked Example 1

A spinner is spun 50 times. The results are shown below.