| Date | May 2018 | Marks available | 2 | Reference code | 18M.2.sl.TZ2.1 |
| Level | SL only | Paper | 2 | Time zone | TZ2 |
| Command term | Find | Question number | 1 | Adapted from | N/A |
Question
In a company it is found that 25 % of the employees encountered traffic on their way to work. From those who encountered traffic the probability of being late for work is 80 %.
From those who did not encounter traffic, the probability of being late for work is 15 %.
The tree diagram illustrates the information.
The company investigates the different means of transport used by their employees in the past year to travel to work. It was found that the three most common means of transport used to travel to work were public transportation (P ), car (C ) and bicycle (B ).
The company finds that 20 employees travelled by car, 28 travelled by bicycle and 19 travelled by public transportation in the last year.
Some of the information is shown in the Venn diagram.
There are 54 employees in the company.
Write down the value of a.
Write down the value of b.
Use the tree diagram to find the probability that an employee encountered traffic and was late for work.
Use the tree diagram to find the probability that an employee was late for work.
Use the tree diagram to find the probability that an employee encountered traffic given that they were late for work.
Find the value of x.
Find the value of y.
Find the number of employees who, in the last year, did not travel to work by car, bicycle or public transportation.
Find \(n\left( {\left( {C \cup B} \right) \cap P'} \right)\).
Markscheme
a = 0.2 (A1)
[1 mark]
b = 0.85 (A1)
[1 mark]
0.25 × 0.8 (M1)
Note: Award (M1) for a correct product.
\( = 0.2\,\,\,\left( {\,\frac{1}{5},\,\,\,20\% } \right)\) (A1)(G2)
[2 marks]
0.25 × 0.8 + 0.75 × 0.15 (A1)(ft)(M1)
Note: Award (A1)(ft) for their (0.25 × 0.8) and (0.75 × 0.15), (M1) for adding two products.
\( = 0.313\,\,\,\left( {0.3125,\,\,\,\frac{5}{{16}},\,\,\,31.3\% } \right)\) (A1)(ft)(G3)
Note: Award the final (A1)(ft) only if answer does not exceed 1. Follow through from part (b)(i).
[3 marks]
\(\frac{{0.25 \times 0.8}}{{0.25 \times 0.8 + 0.75 \times 0.15}}\) (A1)(ft)(A1)(ft)
Note: Award (A1)(ft) for a correct numerator (their part (b)(i)), (A1)(ft) for a correct denominator (their part (b)(ii)). Follow through from parts (b)(i) and (b)(ii).
\( = 0.64\,\,\,\left( {\frac{{16}}{{25}},\,\,64{\text{% }}} \right)\) (A1)(ft)(G3)
Note: Award final (A1)(ft) only if answer does not exceed 1.
[3 marks]
(x =) 3 (A1)
[1 Mark]
(y =) 10 (A1)(ft)
Note: Following through from part (c)(i) but only if their x is less than or equal to 13.
[1 Mark]
54 − (10 + 3 + 4 + 2 + 6 + 8 + 13) (M1)
Note: Award (M1) for subtracting their correct sum from 54. Follow through from their part (c).
= 8 (A1)(ft)(G2)
Note: Award (A1)(ft) only if their sum does not exceed 54. Follow through from their part (c).
[2 marks]
6 + 8 + 13 (M1)
Note: Award (M1) for summing 6, 8 and 13.
27 (A1)(G2)
[2 marks]
