Statistics

Confusing Theoretical and Experimental Probability

Students use what happened in a small experiment as if it must equal the theoretical probability.

Quick check

Why students make it

A small set of trials can feel like it shows the true probability. Students forget that random results can vary, especially when the number of trials is small.

The rule done right

Theoretical probability comes from the possible outcomes, such as P(heads)=12P(\text{heads}) = \frac{1}{2} for a fair coin. Experimental probability comes from data, such as P(heads)=number of headsnumber of flipsP(\text{heads}) = \frac{\text{number of heads}}{\text{number of flips}}.

Related resources

probabilityexperimental-probabilitytheoretical-probability