| Date | May 2010 | Marks available | 2 | Reference code | 10M.1.sl.TZ2.6 |
| Level | SL only | Paper | 1 | Time zone | TZ2 |
| Command term | Find | Question number | 6 | Adapted from | N/A |
Question
A group of 30 students were asked about their favourite topping for toast.
18 liked peanut butter (A)
10 liked jam (B)
6 liked neither
Show this information on the Venn diagram below.
Find the number of students who like both peanut butter and jam.
Find the probability that a randomly chosen student from the group likes peanut butter, given that they like jam.
Markscheme
OR 
(A2) (C2)
Note: Award (A2) for 3 correctly placed values, and no extras (4 need not be seen), (A1) for 2 correctly placed values, (A0) for 1 or no correctly placed values.
[2 marks]
18 + 10 + 6 = 30 (M1)
= 4 (A1) (C2)
[2 marks]
\({\text{P}}(A|B) = \frac{4}{{10}}\left( {\frac{2}{5},{\text{ }}0.4,{\text{ }}40{\text{ }}\% } \right)\) (A1)(ft)(A1) (C2)
Note: Award (A1)(ft) for their numerator from part (b), (A1) for denominator.
[2 marks]
Examiners report
The first two parts of this question were well answered with most candidates completing the Venn diagram correctly and finding the number in the intersection. The final part, requiring a conditional probability to be found, proved more difficult as many candidates tried to use the formula, when all that was required was to look at the values in the Venn diagram. Follow through marks were awarded in part (c) for values correctly used from parts (a) and (b).
The first two parts of this question were well answered with most candidates completing the Venn diagram correctly and finding the number in the intersection. The final part, requiring a conditional probability to be found, proved more difficult as many candidates tried to use the formula, when all that was required was to look at the values in the Venn diagram. Follow through marks were awarded in part (c) for values correctly used from parts (a) and (b).
The first two parts of this question were well answered with most candidates completing the Venn diagram correctly and finding the number in the intersection. The final part, requiring a conditional probability to be found, proved more difficult as many candidates tried to use the formula, when all that was required was to look at the values in the Venn diagram. Follow through marks were awarded in part (c) for values correctly used from parts (a) and (b).
