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The Probability Scale

FoundationHigherAQAEdexcel

Understand The Probability Scale for GCSE Statistics with this free worksheet and full mark scheme — Foundation and Higher exam-style questions with worked answers for AQA and Edexcel. Probability is measured on a scale from 0 (impossible) to 1 (certain).

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These worksheets and mark schemes are original, written for Virtus Academy and checked against the current AQA and Edexcel specifications. Every worksheet comes with a full mark scheme.

Foundation

WorksheetFoundation · PDFMark SchemeFoundation · PDF

Higher

WorksheetHigher · PDFMark SchemeHigher · PDF

Topic overview

Probability measures how likely an event is to happen, on a scale from 0 to 1.

A probability of 0 means the event is impossible and cannot happen. A probability of 1 means it is certain and must happen. A probability of 0.5 means the event is as likely to happen as not.

Probabilities can be written as fractions, decimals or percentages, but never as ratios — writing a probability as 1:6 loses the mark. The probabilities of all possible outcomes of an event always sum to 1, which means the probability of an event not happening is \(1 -\) the probability that it does.

Revision notes

The scale

Probability runs from 0 to 1. Zero means impossible; one means certain.

A value of 0.5 means equally likely to happen or not. Values closer to 1 mean more likely; values closer to 0 mean less likely.

How to write probabilities

As a fraction, decimal or percentage.

Never as a ratio — writing 1:6 instead of \(\frac{1}{6}\) loses the mark. A probability can never be greater than 1 or less than 0, so any such answer indicates an error.

The complement

All possible outcomes sum to a probability of 1.

So \(P(\text{not } A) = 1 - P(A)\). If the probability of rain is 0.3, the probability of no rain is \(1 - 0.3 = 0.7\). This is often the quickest route to an answer.

Key points

  • Probability runs from 0 to 1.
  • Zero means impossible.
  • One means certain.
  • Write probabilities as fractions, decimals or percentages.
  • Never write a probability as a ratio.
  • \(P(\text{not } A) = 1 - P(A)\).

Worked examples

Example 1

The probability of rain tomorrow is 0.35. Work out the probability that it does not rain. [2 marks]

Working

\(P(\text{not rain}) = 1 - P(\text{rain}) = 1 - 0.35\)subtract the probability from 1
\(= 0.65\)work out the probability

Example 2

A student writes a probability as 3:10. Explain the error. [2 marks]

Working

A probability must be written as a fraction, decimal or percentage, not as a ratiostate the rule
so it should be written as \(\frac{3}{10}\), 0.3 or 30 per centgive the correct form

Example 3

A student calculates a probability of 1.4. Explain what this shows. [2 marks]

Working

Probability cannot be greater than 1state the rule
so an answer of 1.4 shows an arithmetic error has been madestate what it means

Common mistakes

  • Writing a probability as a ratio.

    Use a fraction, decimal or percentage.

  • Giving a probability greater than 1.

    This is impossible and indicates an error.

  • Confusing impossible with unlikely.

    Impossible means probability exactly 0.

  • Forgetting the complement shortcut.

    \(1 - P(A)\) is often the quickest route.

Exam tips

  • Check every probability lies between 0 and 1.
  • Never write a probability as a ratio.
  • Use \(1 - P(A)\) for 'not' questions.
  • Give the answer in the form the question uses.

Key terms

Probability
A measure of how likely an event is, from 0 to 1.
Impossible
Having a probability of 0.
Certain
Having a probability of 1.
Complement
The event not happening, with probability \(1 - P(A)\).

Related topics

Written and reviewed against the current AQA and Edexcel specifications. Spotted an error? Let us know.