Relative and expected frequencies

Maths · Probability. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.

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The idea

Sometimes outcomes are not equally likely, for example with a biased dice or a drawing pin. Then the probability must be estimated from an experiment. The relative frequency of an event is the fraction of the trials in which it happened.

Relative frequency is only an estimate, and it changes each time the experiment is repeated. The more trials there are, the more reliable the estimate is.

Expected frequency works the other way round. If you know the probability, you can predict how many times the event should happen in a given number of trials. This is an average, not a promise: the real result is usually close to it but not exactly equal.

Rules to remember

Common mistake

Students give the count as the probability, or divide by the wrong number. A relative frequency is the count divided by the total number of trials, so it is always between 0 and 1.

Worked example

A machine makes parts. In a sample of 150 parts, 9 are faulty. Estimate how many parts are not faulty in a batch of 2000.

  1. Relative frequency of faulty = 9 ÷ 150 = 0.06.
  2. Estimated P(not faulty) = 1 − 0.06 = 0.94.
  3. Expected number not faulty = 0.94 × 2000 = 1880.

Answer: 1880 parts

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