Experimental probability
Objective. Estimate probability from relative frequency and compare with expectation.
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Learn: the key idea
Experimental probability estimates the likelihood of an event by carrying out trials and recording how often the event actually occurs, rather than relying on theoretical reasoning alone. It is calculated as the number of times the event happened divided by the total number of trials conducted. For example, if a drawing pin lands point-up 18 times out of 50 throws, the experimental probability of landing point-up is 18/50, which simplifies to 9/25. As the number of trials increases, experimental probability usually gets closer to the true theoretical probability, a pattern known as relative frequency stabilising.
Worked example
A spinner is spun 40 times and lands on red 14 times. Find the experimental probability of landing on red, as a fraction in its simplest form.
- 1Identify the number of successful outcomes: 14 times landing on red.
- 2Identify the total number of trials: 40 spins.
- 3Write the probability as a fraction: 14/40.
- 4Simplify by dividing both by their HCF of 2: 7/20.
Answer: 7/20
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Start practisingCommon mistake. Pupils sometimes treat a small number of trials as giving a definitive probability, overstating confidence in results from just a few throws. Always recognise that more trials generally give a more reliable estimate.
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