Foundation January 2019 Paper 2 Q17
17 There are 90 counters in a bag.
Each counter in the bag is either red or blue so that
the number of red counters : the number of blue counters = 2 : 13
Li is going to put some more red counters in the bag so that the probability of taking at random a red counter from the bag is \(\dfrac{1}{3}\)
Work out the number of red counters that Li is going to put in the bag.
(4)
| Scheme | Marks |
|---|---|
| 90 ÷ (2 + 13) (= 6) or \(\dfrac{12 + x}{90 + x} = \dfrac{1}{3}\) | M1 |
| “6” × 2 (= 12) or “6” × 13 (= 78) or \(3(12 + x) = 90 + x\) | M1 |
| (“78” ÷ 2) – “12” or \(2x = 54\) or “78” × 3/2 – “78” – “12” oe | M1 |
| 27 | A1 |
| (4) | |
| (4 marks) |
Notes
M1: M2 for \(\dfrac{2}{15} \times 90\) (= 12) or \(\dfrac{13}{15} \times 90\) (= 78)
M1: dep on a correct method for “78” and “12”