Higher November 2018 Paper 1 Q10
10. Mike wants to find out how many fish there are in his lake.
On Monday evening,
Mike captured a random sample of 100 fish and tagged them.
He then released them back into the water.
On Tuesday evening,
Mike captured a second random sample of 50 fish and counted the number that had been tagged.
He found that 10 of the fish in the second sample had been tagged.
Mike will allow fishing at his lake when there are more than 800 fish.
You may assume that the number of fish in the lake stays the same between the two samples being taken.
Should Mike allow fishing at his lake?
Show calculations to justify your decision. [3]
Decision: Allow fishing ☐ Do not allow fishing ☐
| Scheme | Marks | Comments |
|---|---|---|
| (Proportion of tagged fish in sample is) \(\dfrac{10}{100}\left(=\dfrac{1}{10}\right)\) or equivalent or (Proportion of sample tagged is) \(\dfrac{10}{50}\) or equivalent | M1 | Allow for e.g. ’10 tagged out of 50’ |
| \(\dfrac{10}{50} = \dfrac{100}{500}\) or \(\dfrac{10}{100} = \dfrac{50}{500}\) or 20% (of population) is 100 (fish) or equivalent | M1 | Implies the first M1; allow for e.g. ‘100 tagged out of 500’; allow \(\dfrac{100}{x} = \dfrac{10}{50}\) or \(\dfrac{50}{x} = \dfrac{10}{100}\) or equivalent to score M1 M1 |
| 500 (fish) and do not allow fishing ticked or indicated | A1 | CAO |
| (3) |