| Date | May 2009 | Marks available | 2 | Reference code | 09M.2.sl.TZ2.1 |
| Level | SL only | Paper | 2 | Time zone | TZ2 |
| Command term | Find | Question number | 1 | Adapted from | N/A |
Question
A survey of 100 families was carried out, asking about the pets they own. The results are given below.
56 owned dogs (S)
38 owned cats (Q)
22 owned birds (R)
16 owned dogs and cats, but not birds
8 owned birds and cats, but not dogs
3 owned dogs and birds, but not cats
4 owned all three types of pets
Draw a Venn diagram to represent this information.
Find the number of families who own no pets.
Find the percentage of families that own exactly one pet.
A family is chosen at random. Find the probability that they own a cat, given that they own a bird.
Markscheme
(A1)(A1)(A1)(A1)(A1)
Note: Award (A1) for rectangle (U not required), (A1) for 3 intersecting circles, (A1) for 4 in central intersection, (A1) for 16, 3, 8 and (A1) for 33, 10, 7 (ft) if subtraction is carried out, or for S(56), Q(38) and R(22) seen by the circles.
[5 marks]
100 − 81 (M1)
19 (A1)(ft)(G2)
Note: Award (M1) for subtracting their total from 100.
[2 marks]
\(33 +10 + 7\) (M1)
Note: Award (M1) for adding their values from (a).
\(\left( {\frac{{50}}{{100}}} \right) \times 100{\text{ }}\% \) (A1)(ft)
50 % (50) (A1)(ft)(G3)
[3 marks]
P (own a cat given they own a bird) \( = \frac{{12}}{{22}}\left( {0.545,\frac{6}{{11}}} \right)\) (A1)(ft)(A1)(ft)
Note: Award (A1)(ft) for the numerator, (A1)(ft) for the denominator.
[2 marks]
Examiners report
Most candidates began the paper well by correctly drawing the Venn diagram and answering parts (b) and (c) correctly.
Most candidates began the paper well by correctly drawing the Venn diagram and answering parts (b) and (c) correctly.
Most candidates began the paper well by correctly drawing the Venn diagram and answering parts (b) and (c) correctly.
Conditional probability has proved difficult for many candidates; only a very small part of the candidates scored full marks for this part.
