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Basic ProbabilityAQA GCSE Maths: Revision notes

Section 1

How Do We Record and Describe Probability Experiments?

The results (outcomes) of probability experiments can be recorded, described and analysed using tables and frequency trees, which organise how often each outcome occurred.

Randomness, fairness and equally likely events are used to calculate the expected outcomes of future experiments — for example, predicting how many times a fair coin should land on heads over 100 tosses.

Key termsoutcomeexpected outcome
Example

If a fair coin is tossed 50 times, the expected number of heads is 50×0.5=2550 \times 0.5 = 25.

Section 2

How Does Relative Frequency Relate to Theoretical Probability?

Relative frequency is calculated from real experimental results: number of successful trialstotal number of trials\frac{\text{number of successful trials}}{\text{total number of trials}}. As the number of trials increases, the relative frequency tends to get closer to the theoretical probability.

Probabilities are always written on a scale from 0 to 1, and can be expressed as fractions, decimals or percentages.

Key termsrelative frequencytheoretical probability

Section 3

What Rules Apply to Sets of Outcomes?

  • The probabilities of an exhaustive set of outcomes (every possible outcome) always sum to 1
  • The probabilities of an exhaustive set of mutually exclusive events (events that cannot happen at the same time) also sum to 1

These rules let you find a missing probability if you know all the others.

Key termsexhaustive outcomesmutually exclusive events
Example

If P(rain)=0.3P(\text{rain}) = 0.3, then P(no rain)=1−0.3=0.7P(\text{no rain}) = 1 - 0.3 = 0.7, since these two outcomes are exhaustive.

Section 4

How Do We Use Diagrams to Enumerate Outcomes?

Tables, grids and Venn diagrams are used to systematically list (enumerate) sets and combinations of outcomes. A theoretical possibility space (e.g. a sample space diagram or grid) lists every equally likely outcome of a single or combined experiment, which can then be used to calculate theoretical probabilities directly by counting favourable outcomes over total outcomes.

Key termspossibility space
Exam tip

For two dice, a possibility space grid has 36 equally likely outcomes — draw it as a 6×6 table to count favourable outcomes accurately.

Must Know

  • Probabilities always lie between 0 and 1, and can be written as fractions, decimals or percentages
  • The probabilities of an exhaustive set of outcomes (or mutually exclusive events) always sum to 1
  • Relative frequency = successful trials ÷ total trials; it approaches theoretical probability as trials increase
  • Expected outcome = probability × number of trials
  • Use tables, frequency trees, grids and Venn diagrams to organise and enumerate outcomes systematically
  • A possibility space lists every equally likely outcome, letting you calculate theoretical probability directly

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