Foundation June 2022 Paper 2 Q18
18 A bag only contains red marbles, blue marbles and yellow marbles.
- The probability of picking a red marble is \(\dfrac{2}{5}\).
- There are nine yellow marbles.
- The probability of picking a blue marble is three times as likely as picking a yellow marble.
Work out the total number of marbles in the bag.
You must show your working. [5]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| 60 with correct working | 5 | “correct working” requires at least M2 | |
| M4 for \(36 \times \dfrac{5}{3}\) oe or \(9 \times \dfrac{20}{3}\) oe or \(27 \times \dfrac{20}{9}\) oe or \(24 \times \dfrac{5}{2}\) oe or M3 for \(\dfrac{2}{5} + \dfrac{9}{n} + \dfrac{3 \times 9}{n}\) [= 1] oe or \(\dfrac{3}{5} = \dfrac{9 + 3 \times 9}{n}\) oe or \(\dfrac{1}{4}\) of \(\dfrac{3}{5} = \dfrac{9}{n}\) oe or \(\dfrac{3}{4}\) of \(\dfrac{3}{5} = \dfrac{3 \times 9}{n}\) oe or M2 for \(\dfrac{3 \times 9}{n} + \dfrac{9}{n}\) oe or M1 for \(\dfrac{3 \times 9}{n}\) oe | M4 for any fully correct method e.g. For M3 accept e.g. \(\dfrac{3}{5} = 36\), \(\dfrac{3}{20} = 9\), \(\dfrac{9}{20} = 27\) or \(\dfrac{2}{5} = 24\) oe, \(x = \dfrac{3}{20}\) oe (where \(x\) is probability of Y) M2 for \(3x + x = \dfrac{3}{5}\) oe (from \(x = \text{P(Y)}\)) | ||
| OR M2 for [no. of B + Y =] \(9 + 3 \times 9\) oe or M1 for [no. of B =] \(3 \times 9\) oe B2 for no. of red = 24 or M1 for ratio of R : B + Y = 2 : 3 oe | M2 implied by [no. B + Y =] \(9 + 27\) or 36 M1 for e.g. R = \(\dfrac{2}{5}\), B + Y = \(\dfrac{3}{5}\) | ||
| OR M2 for [no. of B + Y =] \(9 + 3 \times 9\) oe or M1 for [no. of B =] \(3 \times 9\) oe M1 \(\dfrac{3}{5}[n]\) is \(9 + 3 \times 9\) oe A1 \(\dfrac{1}{5}[n]\) is 12 oe If 0 or M1 scored, instead award SC2 for answer 60 with no or insufficient working. If 0 scored, SC1 for \(\dfrac{1}{5}[n]\) oe is 12 with no working. | M2 implied by [no. B + Y =] \(9 + 27\) or 36 May work in equivalent decimals or percentages e.g. 60% is 36, 20% is 12 | ||