Foundation June 2018 Paper 2 Q19
19. Three friends, Jane, Caroline and Eddie, each throw the same dice 40 times.
Their results are shown in the table below.
| Score on the dice | ||||||
|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | 6 | |
| Jane | 8 | 4 | 8 | 8 | 4 | 8 |
| Caroline | 8 | 5 | 7 | 7 | 5 | 8 |
| Eddie | 8 | 2 | 9 | 9 | 4 | 8 |
(a)
Do you think this dice is fair?
You must give a reason for your answer. [1]
Yes ☐ No ☐ Don’t know ☐
(b) What is the best estimate of the probability of scoring a 2 on this dice? [2]
(c) Using Jane’s, Caroline’s and Eddie’s results, how many times would you expect a score greater than 4 to occur in 480 throws of this dice? [2]
| Scheme | Marks | Comments |
|---|---|---|
| Indicates or implies ‘No’ or ‘Don’t know’ with a reason, e.g. ‘No, not all scores are equally likely’, ‘Don’t know, as not enough throws to tell’, ‘No as it shows fewer 2s and 5s’, “No, high numbers of 1 and 6’, ‘No, appears to be biased towards 1 and 6’ | E1 | Accept, e.g. ‘No, should have equal amounts for each number’, Allow, e.g. ‘Don’t know, dice are random so there could be variety in results’, ‘No, if fair all would be 1/6’ |
| Scheme | Marks | Comments |
|---|---|---|
| \(\dfrac{11}{120}\) | B2 | B1 for 11/… or \(\dfrac{4 + 5 + 2}{40 + 40 + 40}\) |
| Scheme | Marks | Comments |
|---|---|---|
| \(\dfrac{37}{120}\) (× 480) | M1 | Accept for \(\dfrac{\text{‘their }4+5+4+8+8+8\text{’}}{\text{‘their }40 + 40 + 40\text{’}}\) (× 480) |
| 148 | A1 | CAO A final answer of 148/480 is M1, A0 |
| (5) |