Probability assumptions

Understand and critically evaluate the core assumptions behind theoretical probability (fairness, equal likelihood, randomness) and recognise when these assumptions fail in real-world contexts.

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Te reo Māori terms

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Learning objective overview

Master Teaching Guide coverage for this objective.

Resources

  • Other: Not in Beta Textbook; no verified external resource found (Master Guide's only listed link was a bled-in Simplifying Algebraic Fractions worksheet, unrelated to this LO)

Terminology

  • probability assumptions
  • fair device
  • equally likely outcomes
  • random experiment
  • bias
  • theoretical probability
  • experimental probability
  • sample size
  • independence

Task goals

  • Identify the three core assumptions of theoretical probability: fair devices, equally likely outcomes, and random processes.
  • Explain why each assumption matters and what happens when an assumption is violated.
  • Distinguish between what is possible and what is likely in a probability context.
  • Use sample size and experimental data to judge whether evidence of bias is convincing.
  • Evaluate probability claims in real-world contexts and identify hidden or unstated assumptions.
  • Critique faulty probability reasoning and explain where the logic breaks down.

Key skills

  • Probability
  • Assumptions
  • Independence
  • Fairness
  • With/without replacement
  • Equally likely

Quick stats

  • 81 total questions
  • 3 difficulty levels
  • Answers included