4MA0 Higher January 2018 Paper 4 Q7
7 There are only white counters, blue counters and red counters in a bag.
Charlie takes at random a counter from the bag.
The probability that he takes a red counter is \(\dfrac{1}{12}\)
The probability that he takes a white counter is three times the probability that he takes a blue counter.
Work out the probability that Charlie takes a blue counter.
(3)
| Scheme | Marks |
|---|---|
| e.g. \(1 - \dfrac{1}{12}\left(= \dfrac{11}{12}\right)\) or \(\dfrac{1}{12} + x + 3x = 1\) | M1 |
| \(\text{“}\dfrac{11}{12}\text{”} \div 4\) or \(\left(1 - \dfrac{1}{12}\right) \div 4\) or \(1 - \dfrac{33}{48}\) | M1 |
| \(\dfrac{11}{48}\) oe | A1 |
| (3) |
Notes
M1: or two fractions that add to \(\dfrac{11}{12}\) eg \(\dfrac{3}{12}, \dfrac{8}{12}\) or 2.75 or an answer of \(\dfrac{8.25}{12}\)
M1: complete method or an answer of \(\dfrac{33}{48}\left(= \dfrac{11}{16}\right)\) or \(\dfrac{2.75}{12}\)
A1: or 0.229(16…) or 22.9(16…)%