20N.1.SL.TZ0.S_1

pestleMathematicsAISLPaper 120N· sl-4-6-combined-mutually-exclusive-conditional-independence-prob-diagramssource ↗

In a class of $30$ students, $19$ play tennis, $3$ play both tennis and volleyball, and $6$ do not play either sport.

The following Venn diagram shows the events “plays tennis” and “plays volleyball”. The values $t$ and $v$ represent numbers of students.

Find the value of $t$ .

[2]

a.i.

Find the value of $v$ .

[2]

a.ii.

Find the probability that a randomly selected student from the class plays tennis or volleyball, but not both.

[2]

Markscheme / solution

valid approach to find $t$ (M1)

eg $t + 3 = 19, 19 - 3$

$t = 16$ (may be seen on Venn diagram) A1 N2

[2 marks]

a.i.

valid approach to find $v$ (M1)

eg $t + 3 + v + 6 = 30, 30 - 19 - 6$

$v = 5$ (may be seen on Venn diagram) A1 N2

[2 marks]

a.ii.

valid approach (M1)

eg $16 + 5$ , $21$ students, $1 - \frac{3 + 6}{30}$ ,

$\frac{21}{30} (= \frac{7}{10})$ A1 N2

[2 marks]

Examiners’ report

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a.i.

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a.ii.

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