Foundation November 2022 Paper 3 Q12
12 Kai has a bag of marbles that are red or blue or green or yellow.
Kai takes a marble at random, records the colour and returns the marble to the bag.
Kai does this 800 times.
The table shows some of the results.
| Colour | Red | Blue | Green | Yellow |
|---|---|---|---|---|
| Frequency | 48 | 80 | 296 | |
| Relative frequency | 0.06 | 0.10 | 0.37 | 0.47 |
(a) Complete the table to show the number of times a yellow marble is taken. [2]
(b)
(i) There are 40 marbles in the bag.
Work out how many blue marbles are likely to be in the bag. [2]
(ii) Is your answer to part (b)(i) likely to be the actual number of blue marbles in the bag?
Give a reason for your answer.
.................... because ........................................ [1]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| 376 | 2 | M1 for \(800 - (48 + 80 + 296)\) or \(80 + 296\) or \(800 \times 0.47\) oe | |
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| (i) 4 | 2 | M1 for \(\dfrac{n}{40} = 0.1\) or \(40 \times 0.1\) oe | Answer \(\dfrac{4}{40}\) implies M1 Do not accept \(\rightarrow\) for \(\times\) M1 for \(\dfrac{80}{800} = \dfrac{4}{40}\) or \(\dfrac{800}{40} = 20\) and \(\dfrac{80}{20}\) |
| (ii) Yes oe and large number of trials oe or No and it is an estimate [of the actual number] oe | 1 | If “Yes” must state or imply large sample. Mention of 800 without saying sample is large is not enough. e.g. Yes, they picked lots of times. 1 Yes, they picked 800 times. 0 If “no” must state or imply estimate e.g. No, the relative frequency is only close to the real value 1 No, it’s an estimate of probability 0 | |