Higher January 2019 Paper 2 Q3
3 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 |
|---|---|
| \(90 \div (2 + 13)\) (= 6) or \(\dfrac{12 + x}{90 + x} = \dfrac{1}{3}\) | M1 |
| \(\text{``}{6}\text{''} \times 2\) (=12) or \(\text{``}{6}\text{''} \times 13\) (=78) or \(3(12 + x) = 90 + x\) | M1 |
| \((\text{``}{78}\text{''} \div 2) - \text{``}{12}\text{''}\) or \(2x = 54\) or \(\text{``}{78}\text{''} \times 3/2 - \text{``}{78}\text{''} - \text{``}{12}\text{''}\) oe | M1 |
| 27 | A1 |
| (4) | |
| (4 marks) |
Notes
M1: dep on a correct method for “78” and “12”
M2 for \(\dfrac{2}{15} \times 90\) (= 12) or \(\dfrac{13}{15} \times 90\) (= 78)