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

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

     (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)

OR

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

Part (a) was done well.

Very few were able to answer (b).