A weather forecaster says the risk of snow tomorrow is 1 in 20. Write down this risk as a percentage.
(Total for Question 1 is 1 mark)
2
A theme park ride has a risk of a technical fault of 1 in 50. Write down this risk as a decimal.
(Total for Question 2 is 1 mark)
3
A charity states the risk of a rare genetic condition is 2 in 500. Write down this risk as a percentage.
(Total for Question 3 is 1 mark)
4
Write down whether this statement is True or False. A risk of 1 in 10 is higher than a risk of 1 in 20.
(Total for Question 4 is 1 mark)
5
A factory reports the risk of a faulty item on Production Line A as 3 in 150. Write down this risk in its simplest 'x in y' form.
(Total for Question 5 is 2 marks)
6
Two smoke alarms state their risk of failure over 10 years: Alarm P: risk = 1 in 40 Alarm Q: risk = 3% Write down which alarm has the higher risk of failure, showing your reasoning.
(Total for Question 6 is 2 marks)
7
A car insurance company states the risk of a claim being made on a policy in a year is 1 in 15. Out of 3000 policyholders, work out the expected number who will make a claim.
(Total for Question 7 is 2 marks)
8
A vaccine trial found that 1 in 250 participants experienced a mild side effect. Out of 12,500 participants, work out the expected number who experienced this side effect.
(Total for Question 8 is 2 marks)
9
A batch of 4000 light bulbs has a risk of being faulty of 1 in 80. Work out the expected number of faulty bulbs in the batch.
(Total for Question 9 is 2 marks)
10
A survey finds that the risk of a household having a smart doorbell is 18%. Out of 250 households, work out the expected number with a smart doorbell.
(Total for Question 10 is 2 marks)
11
A school reports the risk of a student being absent on any given day as 1 in 20. Out of 900 students, work out the expected number absent on a given day.
(Total for Question 11 is 2 marks)
12
Two towns compare their risk of a seasonal infection: Town E: risk = 1 in 300 Town F: risk = 0.4% Write down which town has the higher risk, showing your reasoning.
(Total for Question 12 is 2 marks)
13
A factory tests two batches of phone screens for cracks. Batch 1: risk of a crack = 4 in 200 Batch 2: risk of a crack = 1 in 40 Work out the risk of a crack for each batch as a percentage, and state which batch has the lower risk.
(Total for Question 13 is 3 marks)
14
In a health study, 3000 people took Drug Y and a separate 3000 people took a placebo (a dummy pill with no active ingredient). 45 of the people taking Drug Y reported a headache, compared with 15 of the people taking the placebo. Work out the risk of a headache, as a percentage, for each group, and use these to find the extra risk of a headache caused by taking Drug Y.
(Total for Question 14 is 3 marks)
15
A public health study of 800 people who exercise regularly and 800 people who do not records how many of each group develop a certain health condition over 5 years. 20 of the regular exercisers developed the condition, compared with 60 of those who do not exercise regularly. Work out the risk, as a percentage, for each group, and state how many times higher the risk is for the group that does not exercise regularly.
(Total for Question 15 is 3 marks)
16
An insurance company compares the risk of a claim for two types of policy. Policy X: risk = 1 in 25 Policy Y: risk = 1 in 40 Out of 2000 policyholders on each type, work out the expected number of claims for each policy, and state how many more claims Policy X would be expected to have than Policy Y.
(Total for Question 16 is 3 marks)
17
A trial gives a new painkiller to 4000 patients and a placebo to a separate 4000 patients. 120 of the patients taking the painkiller reported dizziness, compared with 40 of the patients taking the placebo. Work out the risk of dizziness, as a percentage, for each group, work out the extra risk of dizziness caused by the painkiller, and comment on whether this extra risk seems large enough to be a concern.
(Total for Question 17 is 4 marks)
18
Two towns are compared during a norovirus outbreak. Both towns have the same risk of a resident being affected: 1 in 60. Town G has a population of 18,000 and Town H has a population of 42,000. Work out the expected number of people affected in each town, and explain why a newspaper claim that 'Town H is more dangerous because more people were affected there' is misleading, given that both towns share the same risk.
(Total for Question 18 is 4 marks)
Mark scheme · F03D Risk (Foundation): Fluency and Exam Drill
Question 1
B1 5% cao
Answer: 5%
Question 2
B1 0.02 cao
Answer: 0.02
Question 3
B1 0.4% cao
Answer: 0.4%
Question 4
B1 True cao
Answer: True
Question 5
M1 divides both parts by a common factor, e.g. 3 oe
A1 1 in 50 cao
Answer: 1 in 50
Question 6
M1 converts 1 in 40 to 2.5% (or converts 3% to an equivalent 'x in y' form) oe
A1 Alarm Q cao
Answer: Alarm Q has the higher risk.
Question 7
M1 3000 / 15 oe
A1 200 cao
Answer: 200
Question 8
M1 12500 / 250 oe
A1 50 cao
Answer: 50
Question 9
M1 4000 / 80 oe
A1 50 cao
Answer: 50
Question 10
M1 250 x 0.18 oe
A1 45 cao
Answer: 45
Question 11
M1 900 / 20 oe
A1 45 cao
Answer: 45
Question 12
M1 converts 1 in 300 to a percentage, awrt 0.33% oe
A1 Town F cao
Answer: Town F has the higher risk.
Question 13
M1 4/200 = 2% oe
M1 1/40 = 2.5% oe
A1 Batch 1 cao
Answer: Batch 1 = 2%, Batch 2 = 2.5%; Batch 1 has the lower risk.
Question 14
M1 45/3000 = 1.5% oe
M1 15/3000 = 0.5% oe
A1 1% cao
Answer: Drug Y risk = 1.5%, placebo risk = 0.5%; the extra risk of a headache caused by Drug Y is 1%.
Question 15
M1 20/800 = 2.5% oe
M1 60/800 = 7.5% oe
A1 3 times (awrt) cao
Answer: Regular exercisers = 2.5%, non-exercisers = 7.5%; the risk for non-exercisers is 3 times higher.
Question 16
M1 2000/25 = 80 oe
M1 2000/40 = 50 oe
A1 30 more cao
Answer: Policy X = 80 expected claims, Policy Y = 50 expected claims; Policy X would be expected to have 30 more claims.
Question 17
M1 120/4000 = 3% oe
M1 40/4000 = 1% oe
A1 2% cao
B1 sensible comment, e.g. the risk of dizziness triples on the painkiller compared with the placebo, so this extra risk is likely to be a genuine concern worth investigating oe
Answer: Painkiller risk = 3%, placebo risk = 1%; the extra risk of dizziness caused by the painkiller is 2%, and the risk triples compared with the placebo, so it is likely to be considered a genuine concern.
Question 18
B1 Town G = 300 cao
B1 Town H = 700 cao
B1 explains both towns share the same risk per resident, so an individual is equally likely to be affected in either town oe
B1 explains the raw count differs only because Town H has a larger population, not because it is more dangerous oe
Answer: Town G = 300 people, Town H = 700 people affected. The claim is misleading because both towns share the same 1 in 60 risk per resident, so a resident is equally likely to be affected in either town; the higher raw count in Town H is simply because it has a larger population, not because it is more dangerous.