17N.1.SL.TZ0.T_7

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

Rosewood College has 120 students. The students can join the sports club ( $S$ ) and the music club ( $M$ ).

For a student chosen at random from these 120, the probability that they joined both clubs is $\frac{1}{4}$ and the probability that they joined the music club is $\frac{1}{3}$ .

There are 20 students that did not join either club.

Complete the Venn diagram for these students.

N17/5/MATSD/SP1/ENG/TZ0/07.a

[2]

One of the students who joined the sports club is chosen at random. Find the probability that this student joined both clubs.

[2]

Determine whether the events $S$ and $M$ are independent.

[2]

Markscheme / solution

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

N17/5/MATSD/SP1/ENG/TZ0/07.a/M (A1)(A1) (C2)

Note: Award (A1) for 30 in correct area, (A1) for 60 and 10 in the correct areas.

[2 marks]

$\frac{{30}}{{90}}{\text{ }}\left( {\frac{1}{3},{\text{ }}0.333333 \ldots ,{\text{ }}33.3333 \ldots \% } \right)$ (A1)(ft)(A1)(ft) (C2)

Note: Award (A1)(ft) for correct numerator of 30, (A1)(ft) for correct denominator of 90. Follow through from their Venn diagram.

[2 marks]

${\text{P}}(S) \times {\text{P}}(M) = \frac{3}{4} \times \frac{1}{3} = \frac{1}{4}$ (R1)

Note: Award (R1) for multiplying their by $\frac{1}{3}$ .

therefore the events are independent $\left( {{\text{as P}}(S \cap M) = \frac{1}{4}} \right)$ (A1)(ft) (C2)

Note: Award (R1)(A1)(ft) for an answer which is consistent with their Venn diagram.

Do not award (R0)(A1)(ft).

Do not award final (A1) if ${\text{P}}(S) \times {\text{P}}(M)$ is not calculated. Follow through from part (a).

[2 marks]

Examiners’ report

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