Higher June 2024 Paper 1 Q2
2 450 students were asked how they travelled to school on Monday.
Each student walked or travelled by bus or travelled by car or travelled by bicycle.
Each student used just one method of travel.
One of these students is chosen at random.
The table shows information about the probability of each method of travel.
| Method of travel | walk | bus | car | bicycle |
|---|---|---|---|---|
| Probability | 0.20 | \(x\) | \(2x\) | 0.26 |
Work out how many of the 450 students travelled by car.
(4)
| Scheme | Marks |
|---|---|
| 1 – (0.20 + 0.26) oe or 0.54 oe or \(x + 2x + 0.26 + 0.20 = 1\) oe or \(x + 2x = 0.54\) oe | M1 |
\(\dfrac{\text{``}{0.54}\text{''}}{3}(= 0.18)\) or \(\dfrac{2}{3} \times \text{``}{0.54}\text{''}(= 0.36)\) oe or “0.54” × 450 (= 243) | M1 |
| (2 ×) “0.18” × 450 oe or 81 or “0.36” × 450 oe | M1 |
| Working not required, so correct answer scores full marks (unless from obvious incorrect working) Answer: 162 | A1 |
| (4) | |
| (4 marks) |
Notes
M1: showing clear understanding that the total of probabilities is 1
If probabilities are given as percentages then % sign must be seen
M1: for a correct method to find \(x\) or \(2x\)
M1: or for \(\dfrac{81}{450}\) or \(\dfrac{162}{450}\)
2 ALT
| Scheme | Marks |
|---|---|
| (0.2 × 450) + (0.26 × 450) (= 207) oe or 90 + 117 (= 207) or 0.46 × 450 (= 207) | M1 |
| 450 – “207” (= 243) | M1 |
| \(\dfrac{1}{3} \times \text{``}{243}\text{''}\) or 81 or \(\dfrac{2}{3} \times \text{``}{243}\text{''}\) | M1 |
| Working not required, so correct answer scores full marks (unless from obvious incorrect working) Answer: 162 | A1 |
| (4 marks) |
Notes
M1: or for \(\dfrac{81}{450}\) or \(\dfrac{162}{450}\)