Higher June 2024 Paper 2 Q4
4
(a) A fair spinner has six equal sections, each with the number 5, 6, 7 or 8
- Each number appears at least once.
- P(even number) \(=\) P(7)
Work out P(5)
You may use the blank spinner to help you. [3 marks]
(b) A different spinner has ten sections, each labelled A, B, C or D.
| A | B | C | D | |
|---|---|---|---|---|
| Probability | 0.1 | 0.5 | 0.2 | 0.3 |
Give one reason why there must be a mistake in the table. [1 mark]
| Answer | Mark | Comments |
|---|---|---|
| The same number of 7s as even numbers | M1 | any order may be in a list or on the spinner must be at least one 7 |
| 5, 5, 6, 7, 7, 8 | A1 | any order may be in a list or on the spinner may be implied |
| \(\dfrac{2}{6}\) | A1ft | oe fraction, decimal or percentage ft M1A0 with completed spinner or list of six numbers |
Additional guidance
| Ignore simplification or conversion attempt after correct answer seen | |
| Accept 0.33(…) or 33.(…)% for \(\dfrac{2}{6}\) | |
| A list/spinner with blanks and/or using other numbers may still score M1 eg 5, 5, 7, 10 or 5, 6, 7, 7, 8, 9 | M1 |
| \(\dfrac{2}{6}\) with no incorrect working eg 5, 6, 7, 8 on spinner with 2 blanks answer \(\dfrac{2}{6}\) (M1A1 is implied) | M1A1A1 |
| 5, 5, 6, 6, 7, 7 with answer \(\dfrac{2}{6}\) | M1A0A1ft |
| 5, 5, 5, 5, 6, 7 with answer \(\dfrac{4}{6}\) | M1A0A1ft |
| 5, 6, 6, 7, 7, 9 with answer \(\dfrac{2}{6}\) | M1A0A0ft |
| 5, 5, 5, 5, 5, 6 with answer \(\dfrac{5}{6}\) | M0A0A0ft |
| Answer | Mark | Comments |
|---|---|---|
| Valid reason | B1 | eg sum of probabilities is not 1 |
Additional guidance
| Ignore irrelevant statements alongside a correct statement eg the sum of the probabilities is not 1 and the probabilities are not percentages | B1 |
| Do not ignore incorrect statements alongside a correct statement eg the sum of the probabilities is 0.11 not 1 | B0 |
| They add up to 1.1 | B1 |
| They add up to 110% | B1 |
| It is 0.1 too much | B1 |
| One of the probabilities is 0.1 too much | B1 |
| It should be something like 0.1, 0.2, 0.3, 0.4 | B1 |
| B should be 0.4 | B1 |
| They don’t add up correctly | B0 |
| They add up to 0.11 | B0 |
| It’s not a fair spinner | B0 |