| Date | May 2013 | Marks available | 3 | Reference code | 13M.1.sl.TZ1.5 |
| Level | SL only | Paper | 1 | Time zone | TZ1 |
| Command term | Find | Question number | 5 | Adapted from | N/A |
Question
The probability that Tanay eats lunch in the school cafeteria is \(\frac{3}{5}\).
If he eats lunch in the school cafeteria, the probability that he has a sandwich is \(\frac{3}{{10}}\).
If he does not eat lunch in the school cafeteria the probability that he has a sandwich is \(\frac{9}{{10}}\).
Complete the tree diagram below.
[3]
a.
Find the probability that Tanay has a sandwich for his lunch.
[3]
b.
Markscheme
(A1)(A1)(A1) (C3)
Note: Award (A1) for each correct pair of branches.
a.
\(\frac{3}{5} \times \frac{3}{{10}} + \frac{2}{5} \times \frac{9}{{10}}\) (A1)(ft)(M1)
Notes: Award (A1)(ft) for their two correct products, (M1) for addition of their products. Follow through from their tree diagram.
\( = \frac{{27}}{{50}}(0.54,54\% )\) (A1)(ft) (C3)
b.
Examiners report
[N/A]
a.
[N/A]
b.
Syllabus sections
Topic 3 - Logic, sets and probability » 3.7 » Probability of combined events, mutually exclusive events, independent events.
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