| Date | November 2013 | Marks available | 3 | Reference code | 13N.1.sl.TZ0.7 |
| Level | SL only | Paper | 1 | Time zone | TZ0 |
| Command term | Find | Question number | 7 | Adapted from | N/A |
Question
Ramzi travels to work each day, either by bus or by train. The probability that he travels by bus is \(\frac{3}{5}\). If he travels by bus, the probability that he buys a magazine is \(\frac{2}{3}\). If he travels by train, the probability that he buys a magazine is \(\frac{3}{4}\).
Complete the tree diagram.
Find the probability that Ramzi buys a magazine when he travels to work.
Markscheme
(A1)(A1)(A1) (C3)
Note: Award (A1) for each correct pair of branches.
[3 marks]
\(\frac{3}{5} \times \frac{2}{3} + \frac{2}{5} \times \frac{3}{4}\) (A1)(ft)(M1)
Notes: Award (A1)(ft) for two consistent products from tree diagram, (M1) for addition of their products.
Follow through from their tree diagram provided all probabilities are between \(0\) and \(1\).
\(\frac{7}{{10}}{\text{ }}\left( {{\text{0.7, 70% , }}\frac{{42}}{{60}}} \right)\) (A1)(ft) (C3)
[3 marks]
Examiners report
Candidates showed that they were able to place probabilities in the correct position on the tree diagram and many went on to find the correct probability, gaining full marks for this question. Some candidates did not recognize that addition of two products was required. A mistake that was seen too frequently on candidate scripts was giving probabilities, in part (b), that were greater than 1.
Candidates showed that they were able to place probabilities in the correct position on the tree diagram and many went on to find the correct probability, gaining full marks for this question. Some candidates did not recognize that addition of two products was required. A mistake that was seen too frequently on candidate scripts was giving probabilities, in part (b), that were greater than 1.
