Expected outcome (expected value)

Predict how many times an event will occur over n trials using Expected value = n x p, where p is the theoretical probability; emphasise this is a prediction/average, not a guaranteed result, and connect to the Law of Large Numbers (a larger n brings the experimental proportion closer to the theoretical probability).

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Te reo Māori terms

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Learning objective overview

Master Teaching Guide coverage for this objective.

Resources

  • Beta: Skills in Ex 33.04, pg 626 (teacher's note: a very small exercise in the textbook)
  • Dr Austin Maths - Expected Values from Probability Tables Practice GridQuestions PDF · Answers

Terminology

  • Expected outcome
  • Expected value
  • Prediction
  • Average
  • Estimate
  • Random chance

Task goals

  • State and apply the expected-value formula E = n x p to predict how many times an event will occur over n trials.
  • Read a theoretical probability (as a fraction, decimal, or percentage) from a spinner, a probability table, or a stated rate, and use it to find an expected frequency.
  • Combine expected frequencies for two or more outcomes (e.g. "Blue OR Yellow") by adding their probabilities before multiplying by n.
  • Work backwards from a given expected count to find the number of trials n or the underlying probability p.
  • Explain why an actual observed count commonly differs from its expected value, especially over a small number of trials, and that a larger number of trials tends to bring the experimental result closer to the theoretical expectation (Law of Large Numbers).

Key skills

  • Expected value
  • Expected outcome
  • Probability
  • Prediction

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  • 3 difficulty levels
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