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Date	November 2009	Marks available	3	Reference code	09N.1.sl.TZ0.14
Level	SL only	Paper	1	Time zone	TZ0
Command term	Find	Question number	14	Adapted from	N/A

Question

A class consists of students studying Spanish or French or both. Fifteen students study Spanish and twelve study French.

The probability that a student studies French given that she studies Spanish is $\frac{{7}}{{15}}$ .

Draw a Venn diagram in the space below to illustrate this information.

[3]

Find the probability that a student studies Spanish given that she studies one language only.

[3]

Markscheme

(A1)(A1)(A1) (C3)

Note: Award (A1) for a labeled Venn diagram with appropriate sets.

(A1) for 7, (A1) for 8 and 5.

[3 marks]

${\text{P (Spanish / one language only)}} = \frac{{\frac{8}{{20}}}}{{\frac{8}{{20}} + \frac{5}{{20}}}}$ (M1)(A1)(ft)

Note: Award (M1) for substituted conditional probability formula, (A1) for correct substitution. Follow through from their Venn diagram.

$= \frac{8}{{13}}(0.615,{\text{ }}61.5\% )$ (A1)(ft)

${\text{P}}{\text{ (Spanish / one language only)}} = \frac{8}{{8 + 5}}$ (A1)(ft)(M1)

Note: Award (A1) for their correct numerator, (M1) for correct recognition of regions. Follow through from their Venn diagram.

$= \frac{8}{{13}}(0.615,{\text{ }}61.5\% )$ (A1)(ft) (C3)

[3 marks]

Examiners report

Part (a) was done well.

Very few were able to answer (b).

Syllabus sections

Topic 3 - Logic, sets and probability » 3.5 » Venn diagrams and simple applications.

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