Foundation June 2017 Unit 2 Q18
18. A dice is thrown 50 times.
The number shown on the dice is recorded after each throw.
The table below shows the results recorded.
| Number shown on dice | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| Frequency | 9 | 7 | 8 | 7 | 6 | 13 |
(a) The relative frequency of throwing a 1 was calculated as \(\dfrac{9}{50} = 0{\cdot}18\).
What was the relative frequency of throwing a 6?
Give your answer as a decimal. [1]
What was the relative frequency of throwing a 6?
Give your answer as a decimal. [1]
(b) The number 4 was thrown 7 times in the first 50 throws.
Using this fact, calculate how many times you would expect a 4 to be thrown when this dice is thrown 3000 times. [2]
Using this fact, calculate how many times you would expect a 4 to be thrown when this dice is thrown 3000 times. [2]
(c) How many times would you expect a 4 to be thrown when a fair dice is thrown 3000 times? [2]
| Scheme | Marks | Comments |
|---|---|---|
| 0·26 | B1 | B0 for 13/50, 26/100 etc. |
| Scheme | Marks | Comments |
|---|---|---|
| \(\dfrac{7}{50}\) × 3000 or equivalent | M1 | Only allow misread if 300 or 30000 used. |
| = 420 | A1 | 420/3000 gains M1A0. Mark final answer. |
| Scheme | Marks | Comments |
|---|---|---|
| \(\dfrac{1}{6}\) × 3000 or equivalent | M1 | Only allow misread if 300 or 30000 used. |
| = 500 | A1 | 500/3000 gains M1A0. Mark final answer. Allow M1A0 for 480 or 510 or 498 as implying 1/6 to be 0·16 or 0·17 or 0·166. |