Risk (Foundation)
Risk is a measure of how likely an unwanted event is to happen, often given as a probability, a fraction, or a rate such as '1 in n people'. In GCSE Statistics, risk is used to compare how common or how dangerous different events are, for example the risk of a disease or an accident within a population. Risk can be described as absolute (the plain chance of the event happening) or relative (comparing risk between two groups).
Before you start
Make sure you're comfortable with these topics first:
Method
- Write the risk as a probability, fraction, percentage or '1 in n' statement using the numbers given.
- To find absolute risk, divide the number of people affected by the total number of people in the group.
- To compare risks between two groups, calculate the risk for each group separately using the same method.
- To find relative risk, divide one group's risk by the other group's risk.
- Interpret the relative risk in context: a relative risk greater than 1 means the first group has a higher risk than the second.
- Compare risk, not just raw numbers of people affected, since the groups being compared may be different sizes.
Worked example
In a survey of 400 smokers, 20 develop a certain lung condition. In a survey of 500 non-smokers, 5 develop the same condition. (a) Find the risk of developing the condition for smokers and for non-smokers. (b) Find the relative risk of a smoker developing the condition compared with a non-smoker.
- Risk for smokers = 20 divided by 400 = 0.05 = 1 in 20 = 5%.
- Risk for non-smokers = 5 divided by 500 = 0.01 = 1 in 100 = 1%.
- Relative risk = risk for smokers divided by risk for non-smokers = 0.05 divided by 0.01 = 5.
- Final answer: the risk is 5% for smokers and 1% for non-smokers; smokers are 5 times as likely to develop the condition as non-smokers (relative risk = 5).
Practice questions
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Q1Out of 200 people who ate a certain meal, 10 became ill. What is the risk of becoming ill, as a fraction in its simplest form?Show answer
Answer: 1/20 (10/200 simplified).
Q2Express a risk of 1/20 as a percentage.Show answer
Answer: 5%.
Q3In a trial, 3 out of 150 patients taking a new drug had side effects. Write this risk in '1 in n' form.Show answer
Answer: 1 in 50 (3/150 = 1/50).
Q4Group A has a risk of 0.08 of an event happening; Group B has a risk of 0.02. Find the relative risk of Group A compared with Group B.Show answer
Answer: 4 (0.08 divided by 0.02 = 4).
Q5Out of 600 drivers who used a phone while driving, 24 had an accident that year, compared with 9 out of 900 drivers who did not use a phone. Calculate the risk of an accident for each group.Show answer
Answer: Phone users: 4% (24/600 = 0.04); non-users: 1% (9/900 = 0.01).
Q6Using your answers to the previous question, find the relative risk for phone users compared with non-users, and interpret it.Show answer
Answer: 4 (0.04 divided by 0.01); drivers who use a phone are 4 times as likely to have an accident as those who do not.
Exam-style questions
Written in the style of a GCSE Statistics exam paper, with a full mark scheme.
Out of 250 patients given a new vaccine, 5 experienced a mild side effect. Calculate the risk of a patient experiencing the side effect, giving your answer as a percentage.
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In Town A, 45 out of 900 residents were affected by flooding last year. In Town B, 20 out of 500 residents were affected. (a) Calculate the risk of flooding for each town as a percentage. (b) State which town has the higher risk.
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A study of 1200 cyclists who wear helmets finds that 6 had a head injury in a crash. A separate study of 800 cyclists who do not wear helmets finds that 16 had a head injury. (a) Calculate the risk of head injury for each group. (b) Calculate the relative risk of head injury for cyclists without a helmet compared with cyclists with a helmet.
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See real GCSE Statistics past-paper questions, with official mark schemes →
Free printable worksheet
Want more practice on paper? Download the risk (foundation) worksheet pack - 16 pages of exam-style questions with a full mark scheme. One email opens every download in this browser for 14 days - no account, no card. Print it for personal and classroom use.
This topic is chapter 14 of GCSE Statistics Foundation Workbook 2, the whole course as one free printable PDF.
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