| 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.
Find the probability that a student studies Spanish given that she studies one language only.
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)
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]
Examiners report
Part (a) was done well.
Very few were able to answer (b).
