Maths Essentials, Unit 30, Lesson 2 of 5

Expected outcomes and experiments

GCSE Maths, Probability and statistics: trees, experiments, samples and claims, 25 minutes

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Estimate probabilities from experiments, judge which estimate is most reliable, pool results, read a relative frequency graph, and use probabilities to predict expected numbers and profits.

What you will learn

  • Work out relative frequency and use it to predict
  • Explain why more trials give a more reliable estimate, and pool results from several experiments
  • Compare results with the expected number to judge whether something is fair
  • Work out expected numbers for one event, two events together and a game with prizes

Relative frequency and expected numbers

When the outcomes are not equally likely, estimate the probability from an experiment:

relative frequency = number of times it happened ÷ number of trials
expected number = probability × number of trials

  1. a spinner lands on blue 36 times in 120 spins
  2. relative frequency = 36 ÷ 120 = 0.3
  3. in 500 more spins, expect 0.3 × 500 = 150 blues

An expected number is an estimate, not a promise: the real count will usually be a little different.

Working backwards: if a spinner with 10 equal sections is expected to land on red 240 times in 400 spins, then P(red) = 240 ÷ 400 = 3/5, so 3/5 × 10 = 6 sections are red.

If some frequencies are given and one is missing, the missing one is the total number of trials minus the others. A biased spinner's results, not 1/4 or 1/2, are then the probabilities to use: if 2 and 4 together came up 45 times in 150 spins, expect about 45/150 × 400 = 120 even numbers in 400 more spins.

Each throw of a fair dice is independent of the ones before: after four sixes in a row, the probability of a six next time is still 1/6. The dice has no memory.

The rest of this lesson and its 9 practice questions are locked.

In this lesson

  1. Relative frequency and expected numbers
  2. Which estimate is most reliable?
  3. Fair or biased?
  4. Expected profit
  5. Try it: Run an experiment

9 practice questions, marked as you go; about 25 minutes in all.

Key terms

Pool, Last point

In this unit: Probability and statistics: trees, experiments, samples and claims

More probability and statistics: tree diagrams in depth, expected outcomes from experiments, sampling and populations, critiquing charts and claims, and sample spaces in harder contexts.

All of Probability and statistics: trees, experiments, samples and claims

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