Risk and Decision Making
Master Risk and Decision Making 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 used to describe risk and to inform decisions in everyday and financial contexts.
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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.
Topic overview
Risk is the probability that something undesirable happens, and statistics is used to quantify and communicate it.
Absolute risk is the probability of the event occurring. Relative risk compares the risk in one group with another, calculated as the risk in the exposed group divided by the risk in the unexposed group. A relative risk of 2 means the risk is twice as high.
The distinction matters when communicating risk. A doubling of risk sounds alarming, but if the absolute risk rises from 1 in 100 000 to 2 in 100 000 the practical significance is small. Reporting relative risk without absolute risk is a standard way of making a finding sound more dramatic than it is.
Revision notes
Absolute and relative risk
Absolute risk is the probability that the event occurs, such as 3 in 1000.
Relative risk compares two groups: \(\frac{\text{risk in exposed group}}{\text{risk in unexposed group}}\). A relative risk of 2 means twice the risk; 0.5 means half.
Why both are needed
A doubling of relative risk sounds alarming but may be trivial in absolute terms.
A rise from 1 in 100 000 to 2 in 100 000 is a relative risk of 2 but an absolute increase of just 1 in 100 000. Reporting only the relative figure exaggerates the finding.
Using risk in decisions
Decisions weigh the probability of an outcome against its consequences.
A low-probability event with severe consequences may warrant more concern than a high-probability event with minor ones. Expected value calculations combine both.
Key points
- Risk is the probability of an undesirable event.
- Absolute risk is the probability itself.
- Relative risk compares two groups.
- Relative risk = exposed risk ÷ unexposed risk.
- A relative risk of 2 means twice the risk.
- Relative risk alone can be misleading.
Worked examples
Example 1
A risk rises from 4 in 1000 to 6 in 1000. Work out the relative risk. [2 marks]
Working
Example 2
A newspaper reports that a risk has doubled. Explain why this may be misleading. [2 marks]
Working
Example 3
Explain the difference between absolute and relative risk. [2 marks]
Working
Common mistakes
Reporting relative risk without absolute risk.
Both are needed to judge practical significance.
Confusing a relative risk of 2 with a 2 per cent risk.
A relative risk of 2 means twice as likely, not 2 per cent.
Inverting the relative risk fraction.
Exposed group risk goes on top.
Ignoring the consequences of an outcome.
Decisions weigh probability against severity, not probability alone.
Exam tips
- Give both absolute and relative risk when communicating.
- Put the exposed group on top of the fraction.
- Explain why relative risk alone can mislead.
- Consider severity as well as probability in decisions.
Key terms
- Risk
- The probability that an undesirable event occurs.
- Absolute risk
- The probability of the event itself.
- Relative risk
- The ratio of risk between two groups.
- Exposed group
- The group subject to the factor being studied.
Related topics
Written and reviewed against the current AQA and Edexcel specifications. Spotted an error? Let us know.