Higher November 2022 Paper 2 Q20
20 A vending machine has a different item in each section.
It sells
7 drinks, 3 of which are juice
5 snacks, 2 of which are fruit bars
11 meals, 4 of which are salad.
One drink, one snack and one meal are chosen at random.
Show that the probability of getting a juice, a fruit bar and a salad is more than 5% [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| \(7 \times 5 \times 11\) or 385 or \(3 \times 2 \times 4\) or 24 or \(\dfrac{3}{7}\) or \(\dfrac{2}{5}\) or \(\dfrac{4}{11}\) | M1 | oe |
| \(\dfrac{3 \times 2 \times 4}{7 \times 5 \times 11}\) or \(\dfrac{24}{385}\) or 0.062(…) | M1dep | oe eg \(\dfrac{3}{7} \times \dfrac{2}{5} \times \dfrac{4}{11}\) |
| 6.2(...) or 0.062(…) and 0.05 | A1 | allow 6 with M2 scored or allow 0.06 and 0.05 with M2 scored |
| Alternative method 2 | ||
| \(3 \times 2 \times 4\) or 24 | M1 | oe |
| \(0.05 \times 7 \times 5 \times 11\) or \(0.05 \times 385\) or 19(.25) or 19.3 | M1 | oe |
| 24 and 19(.25) or 24 and 19.3 | A1 | |
Additional guidance
| Up to M1 may be awarded for correct work with no answer, or incorrect answer, even if this is seen amongst multiple attempts | |
| Alt 1 6 or 0.06 without M2 scored is A0 | |
| Alt 1 6.2(...) with no working | M2A1 |
| Alt 2 24 and 19 with no working | M2A1 |
| Do not allow any misreads |