AQA · Mathematics · 8300

GCSE Maths: Capture\Recapture

Probability · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths textbook exercise and practice questions for Capture\Recapture (Corbettmaths Video 391), and every card links back to the exact page it came from. Practice tests are drawn from this deck’s own cards. Source material © Corbettmaths — used with attribution.

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  1. What is the capture-recapture formula for estimating population size N?

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    N ≈ (number marked in first sample × size of second sample) ÷ number marked in second sample.

  2. In capture-recapture, the proportion of marked animals in the second sample is assumed to equal the proportion marked in the whole ?.

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    population

  3. Name one assumption of the capture-recapture method.

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    The population is closed — no births, deaths, immigration or emigration between the two samples. (Also acceptable: marks are not lost, marked animals mix randomly, all animals equally likely to be caught.)

  4. Why must marked animals mix randomly before the second sample in capture-recapture?

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    So the second sample is representative — the proportion marked in it then reflects the proportion marked in the whole population.

  5. 80 fish tagged; next day 16 of 250 caught are tagged. Estimate the population.

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    80 × 250 ÷ 16 = 1250 fish.

  6. 24 squirrels tagged; later 11 of 40 caught are tagged. Estimate the population.

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    24 × 40 ÷ 11 ≈ 87 squirrels (rounded to a whole number).

  7. x fish tagged; 9 of 200 recaptured are tagged; estimate is 1200. Find x.

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    x × 200 ÷ 9 = 1200, so x = 1200 × 9 ÷ 200 = 54.

  8. 840 bees marked; 300 recaptured; estimate is 9000. How many recaptured bees were marked?

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    840 × 300 ÷ 9000 = 28 marked bees.

  9. 90 woodlice marked; y recaptured, 12 marked; estimate is 600. Find y.

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    90 × y ÷ 12 = 600, so y = 600 × 12 ÷ 90 = 80.

  10. How do you rearrange the capture-recapture formula to find the number marked in the second sample?

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    Marked in second sample = (marked in first sample × second sample size) ÷ population estimate.

  11. T foxes tagged Monday; Tuesday T+10 located, 5 tagged; T is an eighth of the estimate. Find the estimate.

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    N = T(T+10)/5 and N = 8T, so T+10 = 40, T = 30, N = 240 foxes.

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