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Maths

Experimental Probability: Does Theory Match Reality?

Overview

Students predict, experiment, and compare — discovering through doing why more trials give more reliable probability estimates.

Learning Objective
Students compare theoretical probability with the results of experiments, understand that relative frequency approaches theoretical probability with more trials, and record results systematically.

Resources needed

  • Coins (one per pair)
  • Dice (one per pair)
  • Tally charts
  • Calculator (optional)

Lesson stages

0 / 7 done
  1. 1 Display a fair coin. 'What is the probability of getting heads?' (1/2). 'If I flip it 10 times, how many heads do I expect?' (5). 'What about 100 times?' (50). Record predictions.
  2. 2 Pairs flip a coin 10 times and record results in a tally chart. Count heads. 'Did everyone get exactly 5?' Collect class results — discuss the variation. 'Why didn't everyone get 5?'
  3. 3 Calculate relative frequency (RF) = number of heads ÷ total flips. For 10 flips: e.g. 4/10 = 0.4. Theoretical probability = 0.5. 'They don't match — yet.'
  4. 4 Pairs flip 20 more times (30 total) and recalculate RF. Then combine with another pair for 60 total. Pool class data for ~300 total. Calculate RF each time and record in a table. What happens as trials increase?
  5. 5 Plot RF on a graph as trials increase (x-axis: number of trials, y-axis: RF). Students observe the convergence towards 0.5. 'The more trials, the closer we get to the theoretical probability.'
  6. 6 What is the theoretical probability of rolling a 6? (1/6 ≈ 0.167). Roll 12 times. Calculate RF. Discuss why variation is larger with dice than with a coin.
  7. 7 'Why does a casino always make money in the long run?' Connect experimental probability to real-world contexts. Students write a conclusion explaining what they discovered.

Tap a step to mark it as done.

Variations

  • Use spinners instead of coins for different theoretical probabilities
  • Compare a biased coin (bent) to a fair one
  • Extend to two-event experiments (rolling two dice, summing results)
More information

Display: theoretical probability, experimental probability, relative frequency, trial, outcome, event. Teach the formula: RF = successes ÷ total trials.

Pre-draw the tally chart and RF table. Reduce to coin only (not dice). Provide a sentence frame for the conclusion.

Do students calculate RF correctly (as a decimal or fraction)? Do they observe convergence as trials increase? Can they explain why results vary in small experiments?

Use a single shared coin and dice. Record class-wide results as a group. Students can use pencil-drawn tally charts.

Students may think if they've had 3 tails in a row, the next flip 'must be' heads (gambler's fallacy). Address this directly: each flip is independent.

Activity details
Primary Medium 40 minutes 5 minutes prep Pairs, Small Group Indoor & Outdoor
Topics
Probability Experimental Probability Theoretical Probability Statistics