Foundation June 2025 Paper 3 Q17
17 Sid and Zak each throw the same biased coin.
Here is some information about their throws.
| Sid | 80 throws | Relative frequency of Heads is 0.75 |
|---|---|---|
| Zak | 120 throws | 72 are Heads |
(a) Work out the relative frequency of Heads for the 200 throws. [2 marks]
(b) Which results would give the best estimate of the probability of Heads?
Tick one box.
- Sid’s 80 throws
- Zak’s 120 throws
- All 200 throws
Give a reason for your answer. [1 mark]
| Answer | Mark | Comments |
|---|---|---|
| \(0.75 \times 80\) or 60 | M1 | oe implied by 132 |
| 0.66 or \(\dfrac{132}{200}\) or \(\dfrac{66}{100}\) or \(\dfrac{33}{50}\) | A1 | oe fraction, decimal or percentage |
Additional guidance
| Ignore simplification or conversion attempts after correct answer | |
| 60 from \(\dfrac{72}{120} = 0.60\) | M0 |
| \(\dfrac{80}{120} = 0.66\) | M0 |
| Answer | Mark | Comments |
|---|---|---|
| Ticks All 200 throws and valid reason | B1 | eg ticks All 200 throws and more throws |
Additional guidance
| Valid reason with non-contradictory work | B1 |
| No box ticked but clear indication of correct box stated in working lines or implied within valid reason | B1 |
| Incorrect box ticked | B0 |
| Examples of valid reasons 200 is the most Bigger number of trials (gives a more accurate result) Both sets of results is more More data Shows us how much they both got (referring to both people) How many times it landed for both (referring to both people) Better result by adding (implies better is more) Examples of invalid reasons More possibility it will land on heads Amount of heads out of 200 More accurate |