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GCSE Maths / Edexcel

Probability scale and basic probability

Use the 0 to 1 probability scale, write probabilities as fractions, decimals or percentages, and use the complement rule.

Probability and StatisticsFoundation and HigherGrades 2 to 5Focused skill

Curriculum path: GCSE Maths > Edexcel > Probability and Statistics > Probability scale and basic probability

Pearson Edexcel GCSE Maths Probability P2, P3 and P4: use the probability scale, calculate probabilities and use probabilities that sum to 1.

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Revision notes

Theory, examples, and quick checks.

Keep the method short, then practise straight away. This note is written for GCSE Maths Edexcel students who need clear working and reliable method marks.

Theory

Probability measures how likely an event is. It is written from 0 to 1.

A probability of 0 means impossible. A probability of 1 means certain. A probability of 1/2 means equally likely to happen or not happen.

For equally likely outcomes, probability = number of successful outcomes / total number of outcomes.

Probabilities can be written as fractions, decimals or percentages. For GCSE working, fractions are often the cleanest.

The complement is the probability that an event does not happen. P(not A) = 1 - P(A).

All probabilities for a complete set of outcomes add to 1. This is a key checking step in Edexcel probability questions.

Key ruleP(event) = favourable outcomes / total equally likely outcomes, and P(not event) = 1 - P(event).

Diagram guide

01/21impossibleeven chancecertainprobabilities stay between 0 and 1
Probability scaleEvery probability sits between 0 and 1: impossible, unlikely, even chance, likely and certain.

Worked examples

Simple probability

A fair spinner has 5 equal sections: red, red, blue, green, green. Find P(red).

01/21impossibleeven chancecertainprobabilities stay between 0 and 1
Probability as a fractionCount successful outcomes and total equally likely outcomes.
  1. There are 5 equal sections altogether.
  2. There are 2 red sections.
  3. P(red) = 2 / 5.

Answer: 2/5

Use the complement

The probability that a bus is late is 0.18. Find the probability that it is not late.

01/21impossibleeven chancecertainprobabilities stay between 0 and 1
Probability scaleEvery probability sits between 0 and 1: impossible, unlikely, even chance, likely and certain.
  1. Late and not late are complementary events.
  2. P(not late) = 1 - 0.18.
  3. 1 - 0.18 = 0.82.

Answer: 0.82

Find a missing probability

A bag contains red, blue and yellow counters. P(red) = 0.4 and P(blue) = 0.35. Find P(yellow).

01/21impossibleeven chancecertainprobabilities stay between 0 and 1
Probability scaleEvery probability sits between 0 and 1: impossible, unlikely, even chance, likely and certain.
  1. All probabilities must add to 1.
  2. P(red or blue) = 0.4 + 0.35 = 0.75.
  3. P(yellow) = 1 - 0.75 = 0.25.

Answer: 0.25

Common mistakes

  • Writing a probability bigger than 1.
  • Using the number of successful outcomes as the denominator.
  • Forgetting that all outcomes must be equally likely before using simple counting.
  • Adding instead of subtracting for the complement.
  • Mixing decimals, percentages and fractions without converting.

Quick exercise

Try these before moving to the exam-style questions.

  1. A fair dice is rolled. Find P(rolling a 6).
    01/21impossibleeven chancecertainprobabilities stay between 0 and 1
    Probability scaleEvery probability sits between 0 and 1: impossible, unlikely, even chance, likely and certain.
  2. A fair dice is rolled. Find P(rolling an even number).
    01/21impossibleeven chancecertainprobabilities stay between 0 and 1
    Probability scaleEvery probability sits between 0 and 1: impossible, unlikely, even chance, likely and certain.
  3. P(rain) = 0.3. Find P(no rain).
    01/21impossibleeven chancecertainprobabilities stay between 0 and 1
    Probability scaleEvery probability sits between 0 and 1: impossible, unlikely, even chance, likely and certain.
  4. What probability means impossible?
    01/21impossibleeven chancecertainprobabilities stay between 0 and 1
    Probability scaleEvery probability sits between 0 and 1: impossible, unlikely, even chance, likely and certain.
  5. What probability means certain?
    01/21impossibleeven chancecertainprobabilities stay between 0 and 1
    Probability scaleEvery probability sits between 0 and 1: impossible, unlikely, even chance, likely and certain.
Exam-style questions

Practise the same skill at three levels.

These are original GCSE-style questions with mark schemes, common wrong answers, and AI marking guidance so feedback stays close to exam expectations.

Basic GCSE styleFoundationNon-calculator2 marks

A bag contains 3 red counters and 7 blue counters. One counter is chosen at random. Find P(red).

01/21impossibleeven chancecertainprobabilities stay between 0 and 1
Probability scaleEvery probability sits between 0 and 1: impossible, unlikely, even chance, likely and certain.
simple probabilityfraction probabilityfoundation probability
Standard exam styleFoundation and HigherEither3 marks

The probability that a train is delayed is 0.12. Work out the probability that the train is not delayed.

01/21impossibleeven chancecertainprobabilities stay between 0 and 1
Probability scaleEvery probability sits between 0 and 1: impossible, unlikely, even chance, likely and certain.
complement ruledecimal probabilityprobability scale
ChallengeFoundation and HigherEither4 marks

A spinner has three colours: red, blue and green. P(red) = 0.45 and P(blue) = 0.28. Work out P(green), and explain why your answer is sensible.

01/21impossibleeven chancecertainprobabilities stay between 0 and 1
Probability scaleEvery probability sits between 0 and 1: impossible, unlikely, even chance, likely and certain.
missing probabilityprobability sumsense check