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Date May 2021 Marks available 2 Reference code 21M.2.SL.TZ2.4
Level Standard Level Paper Paper 2 Time zone Time zone 2
Command term Find Question number 4 Adapted from N/A

Question

At a school, 70% of the students play a sport and 20% of the students are involved in theatre. 18% of the students do neither activity.

A student is selected at random.

At the school 48% of the students are girls, and 25% of the girls are involved in theatre.

A student is selected at random. Let G be the event “the student is a girl” and let T be the event “the student is involved in theatre”.

Find the probability that the student plays a sport and is involved in theatre.

[2]
a.

Find the probability that the student is involved in theatre, but does not play a sport.

[2]
b.

Find PGT.

[2]
c.

Determine if the events G and T are independent. Justify your answer.

[2]
d.

Markscheme

EITHER

PS+PT+PS'T'-PST=1  OR  PST=PS'T''          (M1)

0.7+0.2+0.18-PST=1  OR  PST=1-0.18


OR

a clearly labelled Venn diagram        (M1)


THEN

PST=0.08  (accept 8%)              A1

 

Note: To obtain the M1 for the Venn diagram all labels must be correct and in the correct sections. For example, do not accept 0.7 in the area corresponding to ST'.

 

[2 marks]

a.

EITHER

PTS'=PT-PTS=0.2-0.08  OR

PTS'=PTS-PS=0.82-0.7         (M1)

 
OR

a clearly labelled Venn diagram including PSPT and PST         (M1)


THEN

=0.12  (accept 12%)              A1

 

[2 marks]

b.

PGT=PT/GPG  0.25×0.48         (M1)

=0.12             A1

 

[2 marks]

c.

METHOD 1

PG×PT=0.48×0.2=0.096             A1

PG×PTPGT  G and T are not independent             R1

 

METHOD 2

PTG=0.25             A1

PTGPT  G and T are not independent             R1

 

Note: Do not award A0R1.

 

[2 marks]

d.

Examiners report

[N/A]
a.
[N/A]
b.
[N/A]
c.
[N/A]
d.

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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