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Capture recapture practice questions with answers

Higher · Grade 6

A second set of capture recapture questions for GCSE Maths. They are different from the ones on the topic page, so work through both. Try each question, then open the answer to check your working.

More questions

Question 1 Easy

50 were tagged. A later sample of 40 contains 10 tagged. Estimate the population.

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Answer: 200

  1. Set up proportion: N = 50 × 40 / 10.
  2. Calculate 2000 / 10 = 200.
  • Method (1): Set up proportion: N = 50 × 40 / 10.
  • Accuracy (1): Calculate 2000 / 10 = 200.

Question 2 Easy

24 were tagged. A later sample of 25 contains 6 tagged. Estimate the population.

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Answer: 100

  1. Set up proportion: N = 24 × 25 / 6.
  2. Calculate 600 / 6 = 100.
  • Method (1): Set up proportion: N = 24 × 25 / 6.
  • Accuracy (1): Calculate 600 / 6 = 100.

Question 3 Medium

10 tagged out of a sample of 50. What is the tagged fraction in simplest form?

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Answer: 1/5

  1. Write as a fraction: 10 / 50.
  2. Simplify by dividing by 10 to get 1/5.
  • Method (1): Write as a fraction: 10 / 50.
  • Accuracy (1): Simplify by dividing by 10 to get 1/5.

Question 4 Medium

6 tagged out of a sample of 40. What is the tagged fraction in simplest form?

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Answer: 3/20

  1. Write as a fraction: 6 / 40.
  2. Simplify by dividing by 2 to get 3/20.
  • Method (1): Write as a fraction: 6 / 40.
  • Accuracy (1): Simplify by dividing by 2 to get 3/20.

Question 5 Hard

The estimate is 200 from a sample of 40 containing 10 tagged. The number first tagged was

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Answer: 50

  1. Find sample fraction: 10 / 40 = 1/4.
  2. Calculate (1/4) × 200 = 50.
  • Method (1): Find sample fraction: 10 / 40 = 1/4.
  • Accuracy (1): Calculate (1/4) × 200 = 50.

Question 6 Hard

The estimate is 80 from a sample of 20 containing 5 tagged. The number first tagged was

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Answer: 20

  1. Find sample fraction: 5 / 20 = 1/4.
  2. Calculate (1/4) × 80 = 20.
  • Method (1): Find sample fraction: 5 / 20 = 1/4.
  • Accuracy (1): Calculate (1/4) × 80 = 20.

Exam-style question

A longer question with marks, in the style of a written paper. This is a Yumio practice question, not a past paper question.

Exam-style question 13 marks

A population of beetles is estimated at 300. In a second sample of 60 beetles, 15 are tagged. Work out how many beetles were tagged at first.

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Answer: 75

  1. Find the tagged fraction in the sample: 15 / 60.
  2. Simplify 15 / 60 to 1/4.
  3. The original tagged count is 1/4 of total population 300.
  4. Calculate 300 / 4 = 75.
  5. 75 beetles were originally tagged.
  • Method (1): Tagged fraction 15/60 or 1/4
  • Method (1): 300 × 15 / 60 or 300 / 4
  • Accuracy (1): Final answer 75

Quick checks

Short one-step questions. Pick an option before you open the answer.

Check 1

Tagged fraction in the sample estimates the tagged fraction in the

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The tagged fraction in the sample estimates the tagged fraction in the whole population. population.

Check 2

First catch forty, later ten of fifty. The population estimate is

  1. 400
  2. 201
  3. 200
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200 200.

Check 3

First catch thirty, later six of forty. The population estimate is

  1. 200
  2. 201
  3. 199
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200 200, from 30 times 40 over 6.

Check 4

Known population 200, first tagged 40, sample 50. Expected tagged is

  1. 11
  2. 20
  3. 10
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10 10.

Check 5

Known population 120, first tagged 20, sample 30. Expected tagged is

  1. 5
  2. 30
  3. 10
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5 5.

Check 6

Ten tagged in a sample of fifty. The tagged fraction is

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10/50 cancels to 1/5. 1/5.

Check 7

Six tagged in a sample of forty. The tagged fraction is

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6/40 cancels to 3/20. 3/20.

Check 8

Estimate 200, sample 50, 10 tagged. First catch was

  1. 151
  2. 40
  3. 50
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40 40.

Check 9

Estimate 120, sample 30, 5 tagged. First catch was

  1. 20
  2. 40
  3. 120
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20 20.

Check 10

After multiplying the first catch by the sample size, what comes next?

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Then divide by how many of them showed up tagged in the second sample. Then divide by how many of them showed up tagged in the second sample.

Check 11

Why is 50 divided by 10 not the population?

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That drops the number tagged in the first catch. That drops the number tagged in the first catch.

Check 12

The second sample should contain the same tagged

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fraction as the whole population. fraction as the whole population.

Check 13

Twenty tagged first and five found again in thirty. The population estimate is

  1. 120
  2. 121
  3. 240
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120 120.

Check 14

Fifty tagged first and ten found again in forty. The population estimate is

  1. 400
  2. 199
  3. 200
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200 200, from 50 times 40 over 10.

Check 15

Working backwards uses the estimate times the tagged count, divided by the

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Working backwards multiplies the estimate by the tagged count and divides by the sample size. sample size.

Keep going with Capture recapture

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