Higher November 2019 Paper 1 Q11
11. A scientist wants to find out how many coots there are on a lake.
One Monday morning, she captures a random sample of 48 coots and tags them.
She then releases them back onto the lake.
The following Monday morning, she captures a second random sample of 30 coots and counts the number that are tagged.
The scientist finds that 20 of the coots in the second sample are tagged.
Assume that the number of coots on the lake remains constant.
How many coots are there likely to be on the lake?
Show calculations to justify your answer. [3]
| Scheme | Marks | Comments |
|---|---|---|
| (Proportion of tagged coots in sample is) \(\dfrac{20}{48}\left(= \dfrac{5}{12}\right)\) oe or (Proportion of sample tagged is) \(\dfrac{20}{30}\left(= \dfrac{2}{3}\right)\) oe | M1 | |
| \(\dfrac{5}{12} = \dfrac{30}{72}\) or \(\dfrac{2}{3} = \dfrac{48}{72}\) or \(\dfrac{1}{12}\) (of population) is 6 (coots) oe | M1 | Implies the first M1; allow \(\dfrac{30}{x} = \dfrac{20}{48}\) or \(\dfrac{48}{x} = \dfrac{20}{30}\) or \(\dfrac{30 \times 48}{20}\) oe to score M1 M1 |
| 72 | A1 | CAO |
| (3) |