Foundation November 2024 Paper 2 Q12
12 A spinner has five sides numbered 1 to 5.
If the spinner is fair, the probability that it lands on the number 1 is 0.2.
A student spins the spinner 300 times.
(a) Assuming the spinner is fair, use the information to work out how many times the spinner is expected to land on the number 1. [2]
(b) The spinner actually landed on the number 1 on 58 of the 300 spins.
Decide whether or not the result suggests this spinner is likely to be a fair spinner?
Give a reason for your answer.
............................... because ............................... [1]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| 60 | 2 | M1 for \(0.2 \times 300\) oe | e.g. \(\dfrac{300}{5}\). Final answer \(\dfrac{60}{300}\) implies M1 |
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| Fair/Yes oe and valid reason | 1 | FT their 60 from 12(a) to appropriate conclusion with correct reasons. | Candidates must either: compare their answer to 12(a) approximately to the number 58 or compares their 12(a) answer to 58 and correctly explain why the spinner is or isn’t fair or state that 300 spins is enough/a lot of spins Accept “maybe/don’t know because 300 is not enough spins” Do not allow incorrect statements See appendix 1 |
Appendix
APPENDIX 1 Question 12b
| 12(a) | Response | Mark | |
|---|---|---|---|
| A | 60 | Yes – The probability is 60 therefore 58 out of 300 spins is fair (BOD use of “probability” has implied approximation) | 1 |
| B | 60 | I think so – I got 60 if it was fair so being two out is pretty fair. (shows the approximate relationship) | 1 |
| C | 60 | Fair – it is close to my estimate and it wouldn’t 100% land on it every time. (shows the approximate relationship) | 1 |
| D | 60 | Yes – as there is only 5 numbers they should be expected to land on each number roughly the same amount of times (The words “expected” and “roughly” imply the approximate relationship) | 1 |
| E | 60 | Yes – it was expected to land on 1 60 times and it landed 58 times. (Stated both numbers and implied approximation) | 1 |
| F | 60 | Yes – if it was fair it would have landed on one 60 times but it’s close enough. (“Close enough” implies approximation) | 1 |
| G | 60 | Yes – it’s an estimate not a definite answer. (No approximation or comparison) | 0 |
| H | 60 | Yes – unless you spin it infinite times your result will never be 100% correct. (Incorrect can imply fairness from a sample) | 0 |
| I | 60 | No – if it was a completely a fair spinner it would land on one 60 of the 300 spins. (Incorrect is stating that it has to land on one exactly 60 times) | 0 |
| J | 60 | No – 58 landed on 1 meaning the other numbers on the spinner landed will be different amount of times, if it was a fair spinner 60 would be the correct answer. (Incorrect is stating that it has to land on one exactly 60 times) | 0 |
| K | 60 | Yes - It spins 300 times (Not enough - needs to comment that 300 spins is enough to be reliable) | 0 |
| L | 60 | Yes – is inside of 60 times what could land (The use of the word “inside” does not imply approximation) | 0 |
| N | 5 | Yes – if you divide the 300 spins divided by 5 it is 60 and he was almost on 60 so is fair. (Not a strict FT & use of “almost”) | 1 |
| M | 12 | No – it landed on the number 1 too often (Does not compare their 12(a) to justify the “too often” statement) | 0 |
| O | 20 | No – if the spinner was fair it wouldn’t be 58 times (Does not explain why) | 0 |
| P | 50 | No – if it was a fair spinner then it would have landed on number one 49-51 times. (Implied approximation from 49-51) | 1FT |
| Q | 58 | Yes – it lands on the number 1 the exact number of time.(allow ONLY as their answer to 12(a) is 58) | 1FT |
| R | 58 | Yes – because its roughly about 50 spins given for each number (50 is incorrect (should be 60)- no incorrect statements) | 0 |
| S | 75 | Yes – it is not far off (Not enough for approximation as they do not explain which numbers they are comparing) | 0 |