Higher June 2024 Paper 2 Q7
7 Archie flips a biased coin 200 times.
Here is some information about the outcomes after each 50 flips.
| Total number of flips | 50 | 100 | 150 | 200 |
|---|---|---|---|---|
| Number of heads | 10 | 27 | 37 | 52 |
Work out the best estimate for the probability of flipping a head.
Give a reason for your answer. [2 marks]
| Answer | Mark | Comments |
|---|---|---|
| \(\dfrac{52}{200}\) or \(\dfrac{26}{100}\) or \(\dfrac{13}{50}\) | B1 | oe fraction, decimal or percentage eg 0.26 or 26% |
| Valid reason involving the number of trials | B1 | eg it is from using the largest number of flips |
Additional guidance
| 1st B1 Ignore simplification or conversion attempt after correct answer seen eg \(\dfrac{52}{200} = 0.28\) | 1st B1 |
| 52 out of 200 or 52 : 200 | 1st B0 |
| Probability from incorrect working eg \(\dfrac{10 + 30 + 40 + 50}{50 + 100 + 150 + 200} = \dfrac{130}{500}\) | 1st B0 |
| Ignore irrelevant statements alongside a correct statement eg Using most flips and they could have done more | 2nd B1 |
| Do not ignore incorrect statements alongside a correct statement eg Uses all the flips but they could have used 100 flips | 2nd B0 |
| It uses all the flips | 2nd B1 |
| More spins | 2nd B1 |
| 200 is the largest amount of data | 2nd B1 |
| 200 is the highest number | 2nd B1 |
| 200 is the total number of flips | 2nd B0 |
| 200 flips gives 52 heads | 2nd B0 |
| 200 is the final result | 2nd B0 |
| That is the highest number in the table | 2nd B0 |
| The highest results are more accurate | 2nd B0 |
| 100 flips is easier to work out | 2nd B0 |
| He could use any of the results | 2nd B0 |
| B0B1 is possible eg Answer 27% Reason Use the one from most spins | B0B1 |