Foundation November 2024 Paper 2 Q13
13. Four white discs and four grey discs each have whole numbers written on them.
In a game, the discs are turned face down.
A player chooses one white disc and one grey disc at random.
The player’s score is calculated by dividing the bigger number by the smaller number.
(a)
The table below shows some of the numbers on the discs and some possible scores.
Complete all the missing entries. [2]
| Score | |||||
|---|---|---|---|---|---|
| Grey disc | …… | 12 | 3 | 2 | 1·2 |
| 5 | …… | …… | 1·2 | …… | |
| 4 | 4 | 1 | 1·5 | 2·5 | |
| 2 | 2 | …… | 3 | 5 | |
| 1 | 4 | …… | 10 | ||
| White disc | |||||
(b)
To win the game, a player must get a score greater than 2.
(i) Dante plays the game once.
Calculate the probability that he wins the game. [1]
Calculate the probability that he wins the game. [1]
(ii) Jenna played the game 224 times.
How many games would you expect her to win? [2]
How many games would you expect her to win? [2]
| Scheme | Marks | Comments | ||||||||||||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
All missing entries correct.
| B2 | B1 for 4 or 5 entries correct Accept \(1\frac{1}{4}\) or \(\frac{5}{4}\) for 1.25. | ||||||||||||||||||||||||||||||
| Scheme | Marks | Comments |
|---|---|---|
| (i) \(\frac{7}{16}\) or 0.4375 ISW oe | B1 | STRICT FT their four scores B0 for 0.44 without sight of 0.4375 B0 for 7:16 or 7 in 16 or 7 out of 16 |
| (ii) \(\frac{7}{16}\) × 224 oe | M1 | FT ‘their answer to (b)(i)’ provided ≠ \(\frac{1}{2}\) and < 1 |
| = 98 | A1 | FT. Mark final answer. Allow rounded or truncated FT answers. Award M1 A0 for \(\frac{98}{224}\) |
| (5) |