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Section 13.3 · Statistics and probability

Experiments and expected results

Find experimental probabilities from trials, calculate expected numbers, and compare experimental results with theory.

6 teaching slides 41 practice questions Worked answers for every question

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2 · Key words

experimental probabilitySuccesses divided by the number of trials.
theoretical probabilityWhat should happen, worked out from the outcomes.
trialOne go of the experiment.
expected numberProbability × number of trials.
biasWhen outcomes are not equally likely.

3 · Summary of the sectionrevise from this

  • Theoretical probability is what should happen: favourable ÷ total.
  • Experimental probability is what did happen: successes ÷ trials.
  • Expected number = probability × number of trials.
  • The expected number is an average, not a promise. Getting 8 sixes in 60 rolls instead of 10 is perfectly normal.
  • As the number of trials grows, experimental probability usually moves closer to the theoretical value.
  • A small difference is ordinary variation; a large, persistent one suggests bias.
  • When outcomes are not equally likely — a drawing pin, a weighted spinner — only an experiment can give the probability.
  • This is the same idea as sample size in Unit 6: more trials, more trustworthy.
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Video lessons1 videos

Relative Frequency

British corbettmaths

Experimental probability from trials, and how it settles as the number of trials grows.

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4 · Practice41 questions, easiest first

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13.2 Calculating probabilities
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End-of-unit {UNUM} test