17M.1.SL.TZ1.S_1

pestleMathematicsAISLPaper 117M· sl-4-5-probability-concepts-expected-numberssource ↗

In a group of 20 girls, 13 take history and 8 take economics. Three girls take both history and economics, as shown in the following Venn diagram. The values $p$ and $q$ represent numbers of girls.

M17/5/MATME/SP1/ENG/TZ1/01

Find the value of $p$ ;

[2]

a.i.

Find the value of $q$ .

[2]

a.ii.

A girl is selected at random. Find the probability that she takes economics but not history.

[2]

Markscheme / solution

valid approach (M1)

eg $\,\,\,\,\,$ $p + 3 = 13,{\text{ }}13 - 3$

$p = 10$ A1 N2

[2 marks]

a.i.

valid approach (M1)

eg $\,\,\,\,\,$ $p + 3 + 5 + q = 20,{\text{ }}10 - 10 - 8$

$q = 2$ A1 N2

[2 marks]

a.ii.

valid approach (M1)

eg $\,\,\,\,\,$ $20 - p - q - 3,{\text{ }}1 - \frac{{15}}{{20}},{\text{ }}n(E \cap H') = 5$

$\frac{5}{{20}}\,\,\,\left( {\frac{1}{4}} \right)$ A1 N2

[2 marks]

Examiners’ report

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a.i.

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a.ii.

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