19N.1.SL.TZ0.S_2

pestleMathematicsAASLPaper 119N· sl-4-6-combined-mutually-exclusive-conditional-independence-prob-diagramssource ↗

In a class of $30$ students, $18$ are fluent in Spanish, $10$ are fluent in French, and $5$ are not fluent in either of these languages. The following Venn diagram shows the events “fluent in Spanish” and “fluent in French”.

The values $m$ , $n$ , $p$ and $q$ represent numbers of students.

Write down the value of $q$ .

[1]

Find the value of $n$ .

[2]

Write down the value of $m$ and of $p$ .

[3]

Markscheme / solution

$q = 5$ A1 N1

[1 mark]

valid approach (M1)

eg $\left( {18 + 10 + 5} \right) - 30$ , $28 - 25$ , $18 + 10 - n = 25$

$n = 3$ A1 N2

[2 marks]

valid approach for finding $m$ or $p$ (may be seen in part (b)) (M1)

eg $18 - 3$ , $3 + p = 10$

$m = 15$ , $p = 7$ A1A1 N3

[3 marks]

Examiners’ report

[N/A]