Higher November 2024 Paper 5 Q11
11 A bag only contains green, red, blue and yellow discs.
Orla carries out an experiment.
She picks one disc at a time from the bag, records its colour and then returns the disc to the bag.
When she has finished the experiment, Orla works out the relative frequency of each colour.
Some of her results are shown in the table.
| Colour | Green | Red |
|---|---|---|
| Relative frequency | 0.35 | 0.25 |
The relative frequency of the yellow discs was three times the relative frequency of the blue discs.
In total, there are 2000 discs in the bag.
(a) Use this information to find an estimate for the total number of green and yellow discs that are in the bag.
You must show your working. [5]
You must show your working. [5]
(b) Explain why your estimate may not be reliable. [1]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| 1300 with correct working | 5 | ‘Correct working’ requires evidence of M3 Condone 1300 rounded to 1000 as answer for 5 marks | |
| M3 for \((1 - (0.35 + 0.25)) \times \frac{3}{4} \times 2000\) oe M1 for 0.35 × 2000 oe | For M3 accept 600 yellow M1 implied by 700 | ||
| OR B2 for rel freq of yellow disc = 0.3 or for 1200 Green and red discs in bag or M1 for 0.35+ 0.25 + P(y) + P(b) = 1 or better or for (0.35 + 0.25) × 2000 oe | For B2 accept 700 for green and 500 for red M1 for e.g.1 – (0.35 + 0.25) oe | ||
| M2dep for (their 0.3 + 0.35) × 2000 oe or M1dep for (their 0.3 + 0.35) oe If 0 or M1 only scored, instead award SC2 for answer 1300 If 0 scored, award SC1 for 700 | M2dep and M1 dep on at least M1 earned M1dep implied by 0.65 | ||
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| She may not have done the experiment a lot of times oe | 1 | ||