Higher June 2023 Paper 2 Q7
7 In a game,
- an ordinary fair six-sided dice is rolled
- the fair spinner shown is spun.
The score is the dice number substituted into the spinner expression.
(a) Complete the table to show all of the possible scores. [2 marks]
| 1 | 2 | 3 | 4 | 5 | 6 | |
|---|---|---|---|---|---|---|
| \(2x\) | 8 | |||||
| \(3x\) | 6 | |||||
| \(x^2\) | 25 |
(b) A player wins the game if their score is 10 or more.
Work out the probability that they win the game. [1 mark]
(c) The game is played 711 times.
Estimate the number of games that are won. [2 marks]
| Answer | Mark | Comments |
|---|---|---|
| All values correct | B2 | B1 1 or 2 rows correct |
Additional guidance
| B2 |
| Answer | Mark | Comments |
|---|---|---|
| \(\dfrac{8}{18}\) or \(\dfrac{4}{9}\) or 0.44(4…) or 44(.4…)% | B1ft | oe fraction, decimal or percentage ft their table with \(\geqslant 12\) values must be using 18 for the total number of possible scores |
Additional guidance
| Ignore simplification or conversion attempt (not ratio) after correct probability seen | |
| Ratio answer eg 8 : 18, even alongside a correct probability is B0 | |
| ft decimals or percentages must be correct to the same accuracy as in the scheme eg 10 winning values in their table \(\dfrac{10}{18}\) or 0.55(5…) or 0.56 or 0.556 or 55(.5…)% or 56% or 55.6% | B1ft |
| Answer | Mark | Comments |
|---|---|---|
| \(711 \times\) their \(\dfrac{8}{18}\) | M1 | oe ft their probability from (b) or if no probability in (b), ft their table with \(\geqslant 12\) values where \(0 \lt\) their probability \(\lt 1\) probabilities, if rounded in (c), must be truncated or rounded to at least 2 sf |
| 316 | A1 | SC2 395 |
Additional guidance
| Answer 316 | M1A1 |
| \(\dfrac{316}{711}\) on answer line | M1A0 |
| Condone 316 out of 711 | M1A1 |
| Do not treat estimating by rounding as a misread eg1 700 used instead of 711 eg2 (b) 0.44 (c) \(0.4 \times 711\) (rounded to 1sf in (c) for the probability) eg3 (b) 0.4 (c) \(0.4 \times 711\) (follows through their (b)) | M0A0 M0A0 M1A0 |
| Do not allow ft for a ratio from (b) but may ft their (a) instead | |
| For \(0.44 \times 711\), accept \(44\% \times 711\) but do not accept 44% of 711 unless recovered | |
| The method mark may be implied by a ft answer (decimal or truncated to the nearest integer or rounded up to the nearest integer) eg1 (b) \(\dfrac{7}{18}\) (c) 276.5 or 276 or 277 (correct ft method implied using (b)) eg2 (a) completed table has 7 winning values (b) no probability shown (c) 276.5 or 276 or 277 (correct ft method implied using (a)) | M1A0 M1A0 |