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Capture recapture Quiz

Grade 6 • 6P • 10 Questions (30 Marks)

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Score: 0 / 10
Capture recapture — Notes & Worked Examples Show / Hide

Explanation:

Capture-recapture estimates a total population size N. First, M animals are caught, marked, and released. Later, a second sample of n animals is caught and m of them are found to have marks. Assuming the marked animals mixed randomly, equate the two proportions: MN = mn → N = M × nm.

Key assumptions: no births, deaths, or migration between samples; marks do not rub off; and every animal has an equal chance of being caught.

Example 1: A scientist catches 40 fish in a lake, marks them, and releases them. Next day she catches 60 fish and finds 8 are marked. Estimate the total fish population.

Solution:

Set up equal proportions: 40N = 860
Rearrange for N: N = 40 × 608
N = 2400 ÷ 8 = 300
Answer: 300 fish

Example 2: How would the estimate in Example 1 be affected if some of the marks had washed off overnight?

Solution:

Fewer marked fish (a smaller denominator m) would be recorded in the second sample.
Dividing 40 × 60 by a smaller number gives a larger result:
Answer: The population estimate would be too high (an overestimate).
Question 1
[1 mark]
Work out
A biologist catches 50 fish in a lake, marks them, and releases them. The next day she catches 40 fish and finds that 5 of them are marked.
Estimate the total number of fish in the lake.
Worked Solution & Answer
50N = 540 ⇒ N = 50 × 405 = 400 B1
Answer: 400
Question 2
[1 mark]
Work out
A biologist catches 40 fish in a lake, marks them, and releases them. The next day she catches 40 fish and finds that 10 of them are marked.
Estimate the total number of fish in the lake.
Worked Solution & Answer
40N = 1040 ⇒ N = 40 × 4010 = 160 B1
Answer: 160
Question 3
[2 marks]
There are p counters in a bag.
12 of the counters are yellow.
Shafiq takes at random 30 counters from the bag.
5 of these 30 counters are yellow.
Work out an estimate for the value of p.
Worked Solution & Answer
12p = 530 = 16 ⇒ p = 12 × 6 = 72 M1 A1
Answer: 72
Question Paper (PDF) • Mark Scheme (PDF)
Question 4
[3 marks]
Saffron wants to work out an estimate for the total number of fish in a lake.
On Friday, Saffron catches 180 fish from the lake.
She puts a tag on each of these fish and puts them back into the lake.
On Saturday, Saffron catches 305 fish from the same lake.
She finds that 45 of the 305 fish are tagged.
Work out an estimate for the total number of fish in the lake.
Worked Solution & Answer
180 / N = 45 / 305 M2
⇒ N = (180 × 305) ÷ 45 = 4 × 305 = 1220 A1
Answer: 1220
Question Paper (PDF) • Mark Scheme (PDF)
Question 5 Eduqas Jun 2022 1F Q26 / 1H Q8
[3 marks]
Vikram wanted to find out how many moths there were in a small woodland.
One night, Vikram captured a random sample of 12 moths and marked them.
He then released them back into the woodland.
The next night, Vikram captured a second random sample of 30 moths.
He found that 9 of the moths in the second sample had been marked.
Vikram estimated that there were 40 moths in the woodland.
(a) Show that Vikram’s estimate of the number of moths was correct. [2 marks]
(b) Comment on how reliable Vikram’s estimate was likely to be. [1 mark]
Worked Solution & Answer
(a)
Using the capture-recapture ratio: 930 = 12N M1
9N = 12 × 30 = 360 ⇒ N = 3609 = 40. C1
Answer (a): 40 moths
(b)
The sample size is very small, or assumptions such as no moths dying/births or marks rubbing off may not hold. C1
Answer (b): Unreliable due to very small sample sizes (or marks rubbed off / population changes).
Question Paper (PDF) • Mark Scheme (PDF)
Question 6 Eduqas Jun 2017 1H Q3
[4 marks]
The scale drawing below shows a lake.
There are two small islands in the lake at A and B.
The lifeguard station is marked at C.
ABCLakeShore
Swimming is only allowed in the area of the lake that is,
• nearer to A than it is to B and
• less than 60 metres from C.
Using a ruler and a pair of compasses, show accurately on the diagram the area where swimming is allowed.
Shade the area where swimming is allowed.
Use the scale 1 cm represents 10 m.
Worked Solution & Answer
1. Construct perpendicular bisector of AB with compass arcs. M2
2. Draw arc of radius 6 cm from center C. M1
3. Identify and shade the region inside the lake on A's side of the bisector and inside the circle from C. A1
Answer: Region bounded inside the lake by the perpendicular bisector of line segment AB (closer to A) and within an arc of radius 6 cm centered at C, correctly shaded.
Question Paper (PDF) • Mark Scheme (PDF)
Question 7
[4 marks]
Faiza is studying the population of rabbits in a park.
She wants to estimate the number of rabbits in the park.
On Monday she catches a random sample of 20 rabbits in the park, marks each rabbit with a tag and releases them back into the park.
On Tuesday she catches a random sample of 42 rabbits in the park.
12 of the rabbits are marked with a tag.
(a) Find an estimate for the number of rabbits in the park. [3 marks]
(b) Explain why Albie’s estimate cannot be correct. [1 mark]
Worked Solution & Answer
(a)
20 / N = 12 / 42 M2
⇒ N = (20 × 42) ÷ 12 = 70 A1
Answer (a): 70
(b)
He caught 55 rabbits, so there must be at least 55 rabbits in the wood (the sample size cannot be greater than the population)
Answer (b): He caught 55 rabbits, so there must be at least 55 rabbits in the wood (the sample size cannot be greater than the population)
Question Paper (PDF) • Mark Scheme (PDF)
Question 8
[4 marks]
Maria wants to find an estimate for the number of frogs in a lake.
On Saturday she catches 40 of the frogs.
She puts a tag on each frog and releases them.
On Monday she catches 55 of the frogs.
11 of the frogs have tags.
(a) Work out an estimate for the total number of frogs in the lake.
You must show all your working. [3 marks]
(b) State one assumption you have made. [1 mark]
Worked Solution & Answer
(a)
40 / N = 11 / 55 = 1 / 5 M2
⇒ N = 40 × 5 = 200 A1
Answer (a): 200
(b)
No frogs entered or left the lake (or no tags fell off, and the tagged frogs mixed thoroughly)
Answer (b): No frogs entered or left the lake (or no tags fell off, and the tagged frogs mixed thoroughly)
Question Paper (PDF) • Mark Scheme (PDF)
Question 9
[4 marks]
Shirley wants to find an estimate for the number of bees in her hive.
On Monday she catches 80 of the bees.
She puts a mark on each bee and returns them to her hive.
On Tuesday she catches 150 of the bees.
She finds that 25 of these bees have been marked.
(a) Work out an estimate for the total number of bees in her hive. [3 marks]
(b) If Shirley’s assumption is wrong, explain what effect this would have on your answer to part (a). [1 mark]
Worked Solution & Answer
(a)
80 / N = 25 / 150 M2
⇒ N = (80 × 150) ÷ 25 = 80 × 6 = 480 A1
Answer (a): 480
(b)
Her estimate is too high (an overestimate) because fewer marked bees would be counted.
Answer (b): Her estimate is too high (an overestimate) because fewer marked bees would be counted.
Question Paper (PDF) • Mark Scheme (PDF)
Question 10 Practice Set 5 3H Q16
[4 marks]
Clive wants to estimate the number of bees in a beehive.
Clive catches 50 bees from the beehive.
He marks each bee with a dye.
He then lets the bees go.
The next day, Clive catches 40 bees from the beehive.
8 of these bees have been marked with the dye.
(i) Work out an estimate for the number of bees in the beehive. [3 marks]
bees
(ii) Write down any assumptions you have made. [1 mark]
Worked Solution & Answer
(i)
Set up equal fractions for the marked proportion: M1
marked in 1st sampletotal population N = marked in 2nd sample2nd sample size M1
Answer: 250 A1
Answer (i): 250 bees
(ii)
The population of bees did not change and the dye did not rub off
Answer (ii): The population of bees did not change and the dye did not rub off
Question Paper (PDF) • Mark Scheme (PDF)
Score: 0 / 10 (0 / 30 marks)
Capture recapture Worksheets Next: Surds →

Grade 6 Quizzes

14 Topics
6A - Recurring decimals6B - Harder indices
6C - The product rule6D - Repeated change
6E - Triple brackets6F - Parallel and perpendicular
6G - Inequalities on graphs6H - Similar shapes (area and vol)
6J - Negative scale factors6K - Circle theorems
6L - Cumulative frequency6M - Box plots
6N - Combined transformations6P - Capture recapture