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Lesson 55 · GCSE / Key Stage 4 · Maths · Probability

Probability Language and Scales

Use probability words, fractions, decimals and percentages on the 0 to 1 scale.

Qualification: GCSEKey Stage 4Subject: MathsStrand: Probability

GCSE specification fit

Probability Language and Scales is part of GCSE Maths Probability.

Use probability words, fractions, decimals and percentages on the 0 to 1 scale. Questions may ask for direct calculation, interpretation, explanation or clear method in context.

QualificationGCSE Mathematics

Key stageKey Stage 4

StrandProbability

Tier guidanceFoundation and Higher core probability language

What you will learn

Use impossible, unlikely, even chance, likely and certain.
Write probabilities as fractions, decimals and percentages.
Use the 0 to 1 probability scale.
Know that probabilities of exhaustive outcomes add to 1.
Find missing probabilities in simple models.
Use relative frequency and expected outcomes as probability estimates.
Explain how experimental probability can change as the number of trials changes.

Why this matters

This language appears in every probability topic, from spinner questions to tree diagrams.

Prior knowledge

You should already be comfortable with:

Fractions.
Decimals and percentages.
Reading scales.

Clear explanation

Main idea

A probability of 0 means impossible and 1 means certain. An even chance is 0.5, 1/2 or 50%. Values closer to 1 are more likely; values closer to 0 are less likely.

Method

Probabilities can be fractions, decimals or percentages, but they must represent the same amount. All probabilities for a complete set of outcomes add to 1. Relative frequency estimates probability from repeated trials: number of times the event happened divided by total trials.

Exam tip

Use the complement rule for “not” questions: P(not A) = 1 − P(A). Never give a probability below 0 or above 1. For expected outcomes, multiply the probability by the number of trials and check that the result is sensible in context.

Checked diagram: every valid probability sits from 0 to 1, with equivalent fraction, decimal and percentage forms.

Worked examples

Missing probability

A bag gives P(red)=0.35 and P(blue)=0.45. Find P(green).

Answer: 1 − 0.35 − 0.45 = 0.20.

Equivalent forms

Place 3/5 on the probability scale and write it as a decimal and percentage.

Answer: 3/5 = 0.6 = 60%, so it sits just to the right of even chance and is more likely than not.

Expected outcomes

A spinner has probability 0.15 of landing on blue. Estimate the number of blue results in 400 spins.

Answer: 0.15 × 400 = 60, so expect about 60 blue results.

Quick checks

Choose an answer, then check your thinking.

1. What is P(not rain) if P(rain) = 0.35?

0.35 0.65 1.35

2. Which value cannot be a probability?

0 0.8 1.2

Practice questions

Question 1

What probability means certain?

Reveal answer and marking guidance

Answer: 1.

Marking: Certain events always happen.

Question 2

Convert 0.25 to a fraction.

Reveal answer and marking guidance

Answer: 1/4.

Marking: 0.25 = 25/100 = 1/4.

Question 3

If P(win)=0.3, find P(not win).

Reveal answer and marking guidance

Answer: 0.7.

Marking: Complement is 1 − 0.3.

Question 4

Can a probability be 1.2?

Reveal answer and marking guidance

Answer: No.

Marking: Probabilities must be between 0 and 1.

Question 5

A spinner has probabilities 0.18 for red, 0.27 for blue and 0.35 for green. The only other colour is yellow. Find P(yellow).

Reveal answer and marking guidance

Answer: 0.20.

Marking: Exhaustive probabilities add to 1, so P(yellow) = 1 − 0.18 − 0.27 − 0.35 = 0.20.

Question 6

A football team wins 18 of its next 30 similar matches in a simulation. Use this to estimate the probability of a win as a fraction, decimal and percentage.

Reveal answer and marking guidance

Answer: 3/5, 0.6 and 60%.

Marking: Relative frequency is 18/30 = 3/5 = 0.6 = 60%.

Question 7

A biased coin is tossed 200 times. It lands heads 86 times. Estimate P(tails) from this experiment.

Reveal answer and marking guidance

Answer: 114/200 = 57/100 = 0.57.

Marking: Tails occurred 200 − 86 = 114 times, so the relative frequency is 114/200, which simplifies to 57/100.

Question 8

A game has probability 0.35 of a prize on each play. Estimate how many prizes you would expect in 240 plays.

Reveal answer and marking guidance

Answer: 84 prizes.

Marking: Expected number = 0.35 × 240 = 84.

Question 9

A box contains red, blue and green counters. P(red)=0.28 and P(blue)=0.46. Find P(green), then describe the event using probability language.

Reveal answer and marking guidance

Answer: P(green)=0.26, so green is unlikely but still possible.

Marking: Use exhaustive probabilities: 1 − 0.28 − 0.46 = 0.26. Since 0.26 is below 0.5 but above 0, unlikely is a sensible description.

Question 10

A spinner landed on purple 72 times in 300 spins. Estimate P(purple), then estimate the number of purple results in 500 similar spins.

Reveal answer and marking guidance

Answer: P(purple) = 72/300 = 0.24, so expect about 120 purple results in 500 spins.

Marking: Use relative frequency first, then multiply by the new number of trials: 0.24 × 500 = 120.

Answers and marking guidance

The exact practice answers are hidden under each question so you can try first. For probability language and scales, marks usually come from using the 0 to 1 scale correctly, converting between equivalent forms, applying complements, checking that exhaustive outcomes add to 1, and showing relative-frequency or expected-outcome working with the correct number of trials.

Common mistakes

Giving impossible probabilities: values below 0 or above 1 are not valid probabilities.
Mixing forms carelessly: 0.25, 1/4 and 25% are equivalent, but 0.25% is not the same thing.
Forgetting the complement: if an event and its opposite are the only options, their probabilities add to 1.
Using vague words alone: when the question asks for a probability, support words like likely or unlikely with a number.

Extension challenge

Create a GCSE-style question on probability language and scales, solve it, then write one sentence explaining why your method works.

Reveal answer

Example answer: A good answer includes a correct method, a checked final answer and a short reason using the key vocabulary from this lesson.

Exam-board guidance

Probability Language and Scales appears across Foundation and Higher GCSE Maths. Exact contexts vary, but the core skills are stable: use probability vocabulary accurately, place values on the 0 to 1 scale, check complements or missing probabilities, and link experimental evidence to later relative-frequency work.

AQA GCSE Maths

Check every probability is between 0 and 1, use the complement rule when a question says not, and show relative-frequency or expected-outcome working when experimental evidence is given.

OCR GCSE Maths

Convert fractions, decimals and percentages carefully, especially when placing values on a probability scale, estimating chance from trials or scaling a probability to an expected frequency.

Pearson Edexcel GCSE Maths

Expect missing-probability questions where all possible outcomes add to 1, plus worded expected-outcome questions that need probability × number of trials.

Eduqas GCSE Maths

Use impossible, even chance and certain accurately, then support words with a fraction, decimal, percentage or short contextual comparison when asked.

WJEC Wales

Practise explaining whether an event is unlikely, even chance or likely using a numerical probability, context and any experimental evidence given.

CCEA GCSE Maths

Make sure complementary probabilities add to 1 and give probabilities as fractions, decimals or percentages as requested by the unit question.

Next lesson

Next, continue with Listing Outcomes and Sample Space Diagrams.

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