Risk (Foundation) Worksheets, Questions and Revision

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F03 Risk (Foundation)

EDEXCEL 1ST0 · Calculator allowed · about 80 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

1

A doctor tells a patient that the risk of a particular side effect from a new medicine is 1 in 25.

(a)Explain what is meant by a risk of 1 in 25 for this side effect.(1)

(b)Write the risk of 1 in 25 as a fraction.(1)

(c)Write the risk of 1 in 25 as a decimal.(1)

(d)Write the risk of 1 in 25 as a percentage.(1)

(Total for Question 1 is 4 marks)

2

A weather forecaster says, "The risk of rain tomorrow is 1 in 4." Which of these is the best interpretation of this statement?

A) It will definitely rain tomorrow.
B) On average, it rains on 1 day out of every 4 similar days.
C) It will rain for 1 out of the next 4 hours.
D) It will not rain tomorrow.

(Total for Question 2 is 1 mark)

3

For each statement about risk, write down whether it is True or False.

(a)A risk of 1 in 10 means that, on average, 1 out of every 10 people (or trials) will experience the event.(1)

(b)A risk of 1 in 1000 is a greater risk than a risk of 1 in 10.(1)

(c)A risk can be written as a fraction, a decimal or a percentage.(1)

(Total for Question 3 is 3 marks)

4

A theme park ride has a risk of a technical fault stated as 1 in 200 rides.

(a)Out of 1000 rides, work out how many would be expected to have a technical fault, based on this risk.(2)

(b)Out of 5000 rides, work out how many would be expected to have a technical fault.(2)

(Total for Question 4 is 4 marks)

5

Two smoke alarms state their risk of failing over 10 years:

Alarm A: risk of failure = 1 in 40
Alarm B: risk of failure = 1 in 25

(a)Convert both risks to percentages.(2)

(b)State which alarm has the greater risk of failure.(1)

(Total for Question 5 is 3 marks)

6

A vet records the risk of common health issues in a particular breed of dog, shown in the table.

Health issue	Risk
Hip problems	1 in 8
Skin allergy	1 in 5
Eye condition	1 in 20

(a)Write the risk of skin allergy as a percentage.(1)

(b)Write down which health issue has the greatest risk.(1)

(c)A dog breeder has 160 puppies of this breed. Estimate how many would be expected to develop an eye condition.(2)

(Total for Question 6 is 4 marks)

7

The bar chart shows the risk of a manufacturing fault, as a percentage, on four production lines at a factory.

(a)Write down the risk of a fault on production line C.(1)

(b)Write down which production line has the lowest risk of a fault.(1)

(c)Production line B makes 6000 items per day. Work out the number of faulty items expected per day on production line B.(2)

(d)Production line A makes 15000 items per day. Work out the number of faulty items expected per day on production line A.(2)

(Total for Question 7 is 6 marks)

8

Three smoke alarms state their risk of failure over 10 years in different forms:

Alarm X: risk of failure = 1 in 50
Alarm Y: risk of failure = 3%
Alarm Z: risk of failure = 1/20

(a)Write the risk of Alarm Y as a fraction in its simplest form.(1)

(b)Write the risk of Alarm X as a percentage.(1)

(c)Write the risk of Alarm Z as a percentage.(1)

(d)Put the three alarms in order of risk of failure, from lowest to highest.(2)

(Total for Question 8 is 5 marks)

9

An insurance company states that the risk of a claim being made on a car policy in a year is 1 in 15.

(a)Write this risk as a fraction.(1)

(b)Write this risk as a decimal, correct to 3 decimal places.(1)

(c)Write this risk as a percentage, correct to 1 decimal place.(1)

(d)The company insures 4500 cars. Work out an estimate for the number of claims expected in a year.(2)

(Total for Question 9 is 5 marks)

10

A student wants to investigate the statement: "Older drivers have a lower risk of being involved in a car accident than younger drivers."

(a)Plan: Write a suitable question the student could use to plan this investigation.(1)

(b)Collect: Suggest one source of secondary data the student could use to collect data on accident rates by age group.(1)

(c)Process: The student finds that, in one year, 1 in 25 drivers aged 17 to 25 was involved in an accident, compared with 1 in 200 drivers aged over 50. Work out how many times more likely a driver aged 17 to 25 is to be involved in an accident than a driver aged over 50.(2)

(d)Interpret: Write a conclusion the student could make, interpreting this result in the context of the original statement.(1)

(Total for Question 10 is 5 marks)

11

A factory tests two batches of kettles for faults.

Batch 1: risk of a fault = 3 in 100
Batch 2: risk of a fault = 1 in 40

(a)Write the risk of a fault in Batch 1 as a percentage.(1)

(b)Write the risk of a fault in Batch 2 as a percentage.(1)

(c)The factory makes 12000 kettles in Batch 1 and 8000 kettles in Batch 2. Work out the number of faulty kettles expected in each batch.(3)

(d)A manager claims, "Batch 2 is safer because fewer kettles will be faulty." Comment on whether the manager's claim is fully justified.(2)

(Total for Question 11 is 7 marks)

12

Two towns compare their risk of a seasonal infection:

Town C: risk of infection = 1 in 250
Town D: risk of infection = 0.6%

(a)Write the risk for Town D as a fraction in its simplest form.(2)

(b)Write the risk for Town C as a percentage.(1)

(c)State which town has the greater risk of infection, giving a reason.(2)

(d)Town C has a population of 15000 and Town D has a population of 9000. Work out the number of people expected to be infected in each town.(2)

(Total for Question 12 is 7 marks)

13

In a health study, 2000 people took Drug X and a separate 2000 people took a placebo (a dummy pill with no active ingredient) instead. 20 of the people taking Drug X developed a headache as a side effect, compared with 5 of the people taking the placebo.

(a)Work out the risk of a headache for someone taking Drug X. Give your answer as a percentage.(2)

(b)Work out the risk of a headache for someone taking the placebo. Give your answer as a percentage.(2)

(c)Work out the relative risk: how many times as likely is a person taking Drug X to get a headache compared with a person taking the placebo?(2)

(d)A newspaper headline says, "New drug quadruples headache risk!" Use your answers to comment on whether this headline gives a fair and complete picture of the risk to an individual patient.(2)

(Total for Question 13 is 8 marks)

14

A public health study of 500 smokers and 500 people who have never smoked records how many of each group go on to develop a certain lung condition during their lifetime.

Group	Number in group	Number who develop the condition
Smokers	500	60
Never smoked	500	5

(a)Work out the risk of developing the condition for a smoker, as a fraction in its simplest form.(2)

(b)Work out the risk of developing the condition for someone who has never smoked, as a percentage.(2)

(c)A health advisor wants to use these figures to encourage people not to start smoking. Using your answers to parts a and b, write a sentence comparing the risk to smokers and non-smokers that the health advisor could use.(2)

(Total for Question 14 is 6 marks)

15

Two towns are compared during a winter flu outbreak. Both towns have the same risk of a resident being affected: 1 in 40.

Town A has a population of 8000.
Town B has a population of 20000.

(a)Work out the expected number of residents affected in Town A.(2)

(b)Work out the expected number of residents affected in Town B.(2)

(c)A newspaper claims, "Town B is more at risk from flu than Town A, because more people will be affected." Comment on whether this claim is correct, using your answers to parts a and b.(2)

(Total for Question 15 is 6 marks)

16

In a trial, 2500 people were given a flu vaccine and a separate 2500 people were given a placebo (a dummy injection). During the flu season, 25 of the vaccinated people caught flu, compared with 100 of the people who had the placebo.

(a)Work out the risk of catching flu for someone who had the vaccine. Give your answer as a percentage.(2)

(b)Work out the risk of catching flu for someone who had the placebo. Give your answer as a percentage.(2)

(c)Work out the relative risk: how many times as likely is a person who had the placebo to catch flu compared with a person who had the vaccine?(2)

(d)A health website states, "This vaccine cuts your personal risk of catching flu by three-quarters." Use your answers to explain whether this is a fair and accurate way to describe the results.(2)

(e)The vaccine is offered to two clinics: Clinic 1 has 12000 registered patients and Clinic 2 has 3000 registered patients. Assuming nobody at either clinic is vaccinated, use the placebo risk from part b to estimate how many more people would be expected to catch flu at Clinic 1 than at Clinic 2.(3)

(Total for Question 16 is 11 marks)

Mark scheme · F03 Risk

Question 1

(a) B1 correct explanation, e.g. on average 1 out of every 25 patients (who take the medicine) will experience the side effect, oe
(a) Answer: On average, 1 out of every 25 patients who take the medicine will experience the side effect.
(b) B1 1/25 cao
(b) Answer: 1/25
(c) B1 0.04 cao
(c) Answer: 0.04
(d) B1 4% cao
(d) Answer: 4%

Question 2

B1 B cao
Answer: B) On average, it rains on 1 day out of every 4 similar days.

Question 3

(a) B1 True cao
(a) Answer: True
(b) B1 False cao
(b) Answer: False
(c) B1 True cao
(c) Answer: True

Question 4

(a) M1 1000 divided by 200, oe
(a) A1 5 cao
(a) Answer: 5
(b) M1 5000 divided by 200, oe
(b) A1 25 cao
(b) Answer: 25

Question 5

(a) M1 1/40 and 1/25 converted, oe (method shown for at least one)
(a) A1 2.5% and 4% cao (both correct)
(a) Answer: Alarm A = 2.5%, Alarm B = 4%
(b) B1 Alarm B ft (from correct or consistent percentages in part a)
(b) Answer: Alarm B

Question 6

(a) B1 20% cao
(a) Answer: 20%
(b) B1 Skin allergy cao
(b) Answer: Skin allergy
(c) M1 160 divided by 20, oe
(c) A1 8 cao
(c) Answer: 8

Question 7

(a) B1 2.5% cao
(a) Answer: 2.5%
(b) B1 D cao
(b) Answer: D
(c) M1 6000 x 0.04, oe
(c) A1 240 cao
(c) Answer: 240
(d) M1 15000 x 0.01, oe
(d) A1 150 cao
(d) Answer: 150

Question 8

(a) B1 3/100 cao
(a) Answer: 3/100
(b) B1 2% cao
(b) Answer: 2%
(c) B1 5% cao
(c) Answer: 5%
(d) M1 all three risks compared as percentages (2%, 3%, 5%), oe
(d) A1 X, Y, Z cao (in that order)
(d) Answer: X, Y, Z

Question 9

(a) B1 1/15 cao
(a) Answer: 1/15
(b) B1 0.067 awrt
(b) Answer: 0.067
(c) B1 6.7% awrt
(c) Answer: 6.7%
(d) M1 4500 divided by 15, oe
(d) A1 300 cao
(d) Answer: 300

Question 10

(a) B1 any suitable comparative question linking driver age and accident risk, e.g. 'Do drivers aged over 50 have a lower risk of being involved in an accident than drivers aged 17 to 25?', oe
(a) Answer: e.g. Do drivers aged over 50 have a lower risk of being involved in an accident than drivers aged 17 to 25?
(b) B1 any suitable named or described source, e.g. GOV.UK road casualty statistics, an insurance company's claims data, or DVLA/police records, oe
(b) Answer: e.g. GOV.UK road casualty statistics
(c) M1 200 divided by 25, oe
(c) A1 8 (times) cao
(c) Answer: 8 times
(d) B1 conclusion consistent with the 8-times figure supporting the original statement, e.g. 'This supports the statement: drivers aged 17-25 have a much higher (8 times higher) risk of an accident than drivers aged over 50', oe
(d) Answer: e.g. This supports the statement: younger drivers (17-25) have a much higher risk (8 times higher) of being involved in an accident than drivers aged over 50.

Question 11

(a) B1 3% cao
(a) Answer: 3%
(b) B1 2.5% cao
(b) Answer: 2.5%
(c) M1 12000 x 0.03, oe
(c) M1 8000 x 0.025, oe
(c) A1 360 and 200 cao (both correct)
(c) Answer: Batch 1 = 360, Batch 2 = 200
(d) B1 recognises Batch 2 does have fewer faulty kettles overall (200 versus 360) because fewer kettles were made in that batch
(d) B1 recognises the risk (rate) of a fault is actually similar/not much lower for Batch 2 (2.5% versus 3%), so comparing raw numbers alone when batch sizes differ is misleading, oe
(d) Answer: Not fully justified - Batch 2 has fewer faulty kettles only because fewer kettles were made; the risk (rate) of a fault is similar for both batches (3% vs 2.5%).

Question 12

(a) M1 0.6% = 6/1000, oe (unsimplified fraction or equivalent working)
(a) A1 3/500 cao
(a) Answer: 3/500
(b) B1 0.4% cao
(b) Answer: 0.4%
(c) B1 Town D cao
(c) B1 correct reason comparing percentages, e.g. 0.6% is greater than 0.4%, oe (dep on correct town)
(c) Answer: Town D, because 0.6% is greater than 0.4%.
(d) M1 15000 divided by 250 or 9000 x 0.006, oe (method for at least one town)
(d) A1 60 and 54 cao (both correct)
(d) Answer: Town C = 60, Town D = 54

Question 13

(a) M1 20 divided by 2000, oe
(a) A1 1% cao
(a) Answer: 1%
(b) M1 5 divided by 2000, oe
(b) A1 0.25% cao
(b) Answer: 0.25%
(c) M1 1% divided by 0.25% or 20 divided by 5, oe
(c) A1 4 (times) cao
(c) Answer: 4 times
(d) B1 recognises the relative risk figure (4 times) used in the headline is correct/consistent with part c
(d) B1 recognises the headline could still be misleading because the absolute risk stays low (only 1%, i.e. 1 in 100 patients), so almost all patients will not get a headache, oe
(d) Answer: The 'quadruples' figure is correct (relative risk = 4), but it could be misleading on its own because the absolute risk is still only 1% (1 in 100 patients), so most patients will not get a headache.

Question 14

(a) M1 60/500, oe (unsimplified fraction or equivalent working)
(a) A1 3/25 cao
(a) Answer: 3/25
(b) M1 5 divided by 500, oe
(b) A1 1% cao
(b) Answer: 1%
(c) B1 correctly converts/uses both risks as percentages, 12% (smokers) and 1% (never smoked), oe
(c) B1 correct comparison stated, e.g. 'smokers are 12 times more likely to develop the condition than people who have never smoked', oe (dep on correct percentages/relative risk)
(c) Answer: e.g. Smokers are 12 times more likely to develop the condition than people who have never smoked (12% compared with 1%).

Question 15

(a) M1 8000 divided by 40, oe
(a) A1 200 cao
(a) Answer: 200
(b) M1 20000 divided by 40, oe
(b) A1 500 cao
(b) Answer: 500
(c) B1 recognises the claim is not correct/is misleading, since both towns have the same individual risk (1 in 40)
(c) B1 recognises Town B simply has a larger population, so a larger absolute number of people are affected even though the risk to each resident is identical, oe
(c) Answer: The claim is not correct - both towns have the same risk (1 in 40) for each resident. Town B has more people affected only because it has a larger population, not because residents there are more at risk.

Question 16

(a) M1 25 divided by 2500, oe
(a) A1 1% cao
(a) Answer: 1%
(b) M1 100 divided by 2500, oe
(b) A1 4% cao
(b) Answer: 4%
(c) M1 4% divided by 1% or 100 divided by 25, oe
(c) A1 4 (times) cao
(c) Answer: 4 times
(d) B1 recognises the risk falls from 4% (placebo) to 1% (vaccine), a drop of 3 percentage points
(d) B1 recognises this drop is 3/4 (75%) of the original 4% risk, so 'cuts risk by three-quarters' is a fair/accurate description, oe (accept a reasoned alternative view)
(d) Answer: Yes, it is fair - the risk falls from 4% to 1%, and 1% is one quarter of 4%, so the risk has indeed been cut by three-quarters (75%).
(e) M1 12000 x 0.04, oe (=480)
(e) M1 3000 x 0.04, oe (=120)
(e) A1 360 cao (dep on both M marks)
(e) Answer: 360

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