Foundation June 2022 Paper 1 Q15
15 In a bag there are only red discs, blue discs and green discs.
There are 10 red discs.
When one disc is picked at random
\(\text{P(red)} = \dfrac{1}{8}\)
\(\text{P(blue)} = \dfrac{2}{5}\)
How many green discs are in the bag? [4 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| \(10 \times 8\) or 80 | M1 | oe 80 may be seen as a denominator |
| \(\dfrac{2}{5} \times\) their 80 or 32 | M1 | oe their 80 can be any integer \(\gt 10\) 32 will imply M1M1 and may be seen as a numerator |
| their 80 \(-\) their 32 \(-\) 10 or \(\dfrac{38}{80}\) or their 32 \(+\) 10 or 42 | M1dep | oe calculation dep on 2nd M1 42 will imply M1M1M1dep and may be seen as a numerator |
| 38 | A1 | |
| Alternative method 2 | ||
| \(10 \times 8\) or 80 | M1 | oe 80 may be seen as a denominator |
| \(\dfrac{1}{8} + \dfrac{2}{5}\) or \(\dfrac{21}{40}\) or \(1 - \dfrac{1}{8} - \dfrac{2}{5}\) or \(\dfrac{19}{40}\) | M1 | oe |
| their \(\dfrac{21}{40} \times\) their 80 or 42 or their \(\dfrac{19}{40} \times\) their 80 | M1dep | oe calculation dep on M1M1 42 will imply M1M1M1dep and may be seen as a numerator |
| 38 | A1 | |
Additional guidance
| Alt 1 \(\dfrac{2}{5} \times 40 = 15\), \(40 - 15 - 10 = 15\) \(\dfrac{2}{5} \times 40 = 16\), \(16 + 10\) | M0M1M1depA0 M0M1M1depA0 |