| Date | May 2010 | Marks available | 3 | Reference code | 10M.1.sl.TZ1.8 |
| Level | SL only | Paper | 1 | Time zone | TZ1 |
| Command term | Find | Question number | 8 | Adapted from | N/A |
Question
Maria travels to school either by walking or by bicycle. The probability she cycles to school is 0.75.
If she walks, the probability that she is late for school is 0.1.
If she cycles, the probability that she is late for school is 0.05.
Complete the tree diagram below, showing the appropriate probabilities.
Find the probability that Maria is late for school.
Markscheme
(A1)(A1)(A1) (C3)
Note: Award (A1) for 0.25, (A1) for 0.1 and 0.9, (A1) for 0.05 and 0.95
[3 marks]
\({\text{P}}({\text{late}}) = 0.25 \times 0.1 + 0.75 \times 0.05\) (A1)(ft)(M1)
Note: Award (A1)(ft) for two correct products from their diagram and award (M1) for addition of their two products.
\( = 0.0625\left( {\frac{1}{{16}},{\text{ }}6.25\% } \right)\) (A1)(ft) (C3)
[3 marks]
Examiners report
Part (a) of this question was very well answered with many candidates gaining the maximum marks. Many candidates were less successful in part (b) and it seemed as if many of them either gained 3 marks or 0 marks. This shows that students who knew how to approach part (b) were also able to correctly substitute in the formula they used and reach the correct answer. Very few of those students lost the last mark for wrong rounding.
Part (a) of this question was very well answered with many candidates gaining the maximum marks. Many candidates were less successful in part (b) and it seemed as if many of them either gained 3 marks or 0 marks. This shows that students who knew how to approach part (b) were also able to correctly substitute in the formula they used and reach the correct answer. Very few of those students lost the last mark for wrong rounding.
