Higher June 2019 Paper 2 Q18
18 In a bag there are blue discs, green discs and white discs.
There are four times as many blue discs as green discs.
number of blue discs : number of white discs = 3 : 5
One disc is selected at random.
Work out the probability that the disc is either blue or white. [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| (b : g =) 4 : 1 or (b : w =) 6 : 10 or states a number of blue discs that is four times the number of green discs or states a number of blue discs and a number of white discs that are in the ratio 3 : 5 (not 3 and 5) or \(b = 4g\) or \(\dfrac{b}{w} = \dfrac{3}{5}\) | M1 | oe ratio or equation eg (b : g =) 3 : 0.75 or 4 blue 1 green or 6 blue 10 white or \(5b = 3w\) do not allow (b : w =) 3 : 5 |
| Three numbers of the form \(12n\), \(3n\) and \(20n\) where \(n > 0\) or unsimplified fraction equivalent to \(\dfrac{32}{35}\) | A1 | any order may be seen in a ratio or as numbers of discs eg 12 : 3 : 20 or 100 15 60 or 3 0.75 5 or 4 : 1 : \(\dfrac{20}{3}\) or \(\dfrac{12 + 20}{12 + 3 + 20}\) or \(\dfrac{3 + 5}{3 + 0.75 + 5}\) or \(\dfrac{8}{8.75}\) or \(\dfrac{b + \frac{5}{3}b}{b + \frac{5}{3}b + \frac{1}{4}b}\) or \(\dfrac{\frac{8}{3}b}{\frac{35}{12}b}\) |
| \(\dfrac{32}{35}\) or 0.91(4…) or 91.(4…)% | A1 | oe fraction eg \(\dfrac{64}{70}\) |
Additional guidance
| Ignore conversion of a correct fraction to a decimal or percentage | |
| Ignore incorrect simplification of a correct fraction | |
| Answer 32 : 35 | M1A1A0 |
| Final A1 fraction answers must be \(\dfrac{\text{integer}}{\text{integer}}\) | |
| 1 : 4 only scores M1 if indicated as g : b | |
| 10 : 6 only scores M1 if indicated as w : b | |
| 1st M1 may be embedded eg1 b : g : w = 4 : 1 : 10 eg2 b : g : w = 6 : 3 : 10 | M1 M1 |
| Condone 4b : g as an indication of 4 blue and 1 green etc |