Higher June 2022 Paper 5 Q8
8 A bag only contains red marbles, blue marbles and yellow marbles.
- The probability of picking a red marble is \(\frac{2}{5}\).
- 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 \(36 \times \frac{5}{3}\) oe or \(9 \times \frac{20}{3}\) oe or \(27 \times \frac{20}{9}\) oe or \(24 \times \frac{5}{2}\) oe or M3 for \(\frac{2}{5} + \frac{9}{n} + \frac{3 \times 9}{n}\) [= 1] oe or \(\frac{3}{5} = \frac{9 + 3 \times 9}{n}\) oe or \(\frac{1}{4}\) of \(\frac{3}{5} = \frac{9}{n}\) oe or \(\frac{3}{4}\) of \(\frac{3}{5} = \frac{3 \times 9}{n}\) oe or M2 for \(\frac{3 \times 9}{n} + \frac{9}{n}\) oe or M1 for \(\frac{3 \times 9}{n}\) oe | M4 for any fully correct method e.g. For M3 accept e.g. \(\frac{3}{5}\) = 36, \(\frac{3}{20}\) = 9, \(\frac{9}{20}\) = 27 or \(\frac{2}{5}\) = 24 oe, \(x = \frac{3}{20}\) oe ( where \(x\) is probability of Y) M2 for \(3x + x = \frac{3}{5}\) oe (from \(x\) = P(Y)) | ||
| OR | |||
| M2 for [no. of B + Y =] 9 + 3 × 9 oe or M1 for [no. of B =] 3 × 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 = \(\frac{2}{5}\), B + Y = \(\frac{3}{5}\) | ||
| OR | |||
| M2 for [no. of B + Y =] 9 + 3 × 9 oe or M1 for [no. of B = ] 3 × 9 oe M1 \(\frac{3}{5}[n]\) is 9 + 3 × 9 oe A1 \(\frac{1}{5}[n]\) is 12 oe | M2 implied by [no. B + Y =] 9 + 27 or 36 May work in equivalent decimals or percentages eg 60% is 36, 20% is 12 | ||
| If 0 or M1 scored, instead award SC2 for answer 60 with no or insufficient working. If 0 scored, SC1 for \(\frac{1}{5}[n]\) oe is 12 with no working. | |||