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Date May 2021 Marks available 1 Reference code 21M.2.SL.TZ2.1
Level Standard Level Paper Paper 2 Time zone Time zone 2
Command term Write down Question number 1 Adapted from N/A

Question

A medical centre is testing patients for a certain disease. This disease occurs in 5% of the population.

They test every patient who comes to the centre on a particular day.

It is intended that if a patient has the disease, they test “positive”, and if a patient does not have the disease, they test “negative”.

However, the tests are not perfect, and only 99% of people who have the disease test positive. Also, 2% of people who do not have the disease test positive.

The tree diagram shows some of this information.

Write down the value of

Use the tree diagram to find the probability that a patient selected at random

The staff at the medical centre looked at the care received by all visiting patients on a randomly chosen day. All the patients received at least one of these services: they had medical tests (M), were seen by a nurse (N), or were seen by a doctor (D). It was found that:

State the sampling method being used.

[1]
a.

a.

[1]
b.i.

b.

[1]
b.ii.

c.

[1]
b.iii.

d.

[1]
b.iv.

will not have the disease and will test positive.

[2]
c.i.

will test negative.

[3]
c.ii.

has the disease given that they tested negative.

[3]
c.iii.

The medical centre finds the actual number of positive results in their sample is different than predicted by the tree diagram. Explain why this might be the case.

[1]
d.

Draw a Venn diagram to illustrate this information, placing all relevant information on the diagram.

[3]
e.

Find the total number of patients who visited the centre during this day.

[2]
f.

Markscheme

convenience sampling                 (A1)


[1 mark]

a.

95%                A1


[1 mark]

b.i.

1%                A1


[1 mark]

b.ii.

2%                A1


[1 mark]

b.iii.

98%                A1


[1 mark]

b.iv.

0.95×0.02               (M1)

0.019                A1


[2 marks]

c.i.

0.05×0.01+0.95×0.98               (M1)(M1)


Note: Award M1 for summing two products and M1 for correct products seen.


0.932 (0.9315)                A1


[3 marks]

c.ii.

recognition of conditional probability             (M1)

0.05×0.010.05×0.01+0.95×0.98                A1

0.000537  (0.000536768)                A1


Note:
Accept 0.000536 if 0.932 used.


[3 marks]


c.iii.

EITHER
sample may not be representative of population           A1

OR
sample is not randomly selected           A1

OR
unrealistic to think expected and observed values will be exactly equal            A1


[1 mark]

d.

                A1A1A1   


Note:
Award A1 for rectangle and 3 labelled circles and 9 in centre region; A1 for 2, 40, 24; A1 for 18, 1, and 11.


[3 marks]

e.

18+9+1+11+2+40+24              (M1)   

105                        A1

Note:
Follow through from the entries on their Venn diagram in part (e). Working required for FT.


[2 marks]

f.

Examiners report

[N/A]
a.
[N/A]
b.i.
[N/A]
b.ii.
[N/A]
b.iii.
[N/A]
b.iv.
[N/A]
c.i.
[N/A]
c.ii.
[N/A]
c.iii.
[N/A]
d.
[N/A]
e.
[N/A]
f.

Syllabus sections

Topic 4—Statistics and probability » SL 4.6—Combined, mutually exclusive, conditional, independence, prob diagrams
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Topic 4—Statistics and probability

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