Maths Capturerecapture Miss Parnham 1 Capturerecapture 1 Tommy

Maths Capture-recapture Miss Parnham 1

Capture-recapture 1. Tommy captures 40 fish, tags them 2. Annie captures 16 snails in her and returns them to the lake. garden, marks and releases them. The following day he captures 30 fish and finds that 5 of them are tagged. A day later she captures 15 snails and 3 of them are marked. a) What proportion of the fish that Tommy caught on the second day Estimate the snail population in were tagged? Annie’s garden. b) Estimate the total fish population What assumptions did you make? in the lake. 2

Capture-recapture 3. Dexter wants to estimate how 4. Eva catches some rabbits in a field, many buttons are in a jar. tags and releases them. He empties the jar out, marks 50 of The next day she captures 48 rabbits them, then mixes the buttons and 18 of them are tagged. returns them all to the jar. Eva estimates that the field has a He then takes 45 buttons out of the population of 120 rabbits. jar, 6 of them are marked. Use this information to work out how Show Dexter would use this many rabbits Eva initially caught and information to estimate the number tagged. of buttons in the jar. 3

Answers 4

Capture-recapture 1. Tommy captures 40 fish, tags them 2. Annie captures 16 snails in her and returns them to the lake. garden, marks and releases them. The following day he captures 30 fish and finds that 5 of them are tagged. A day later she captures 15 snails and 3 of them are marked. a) What proportion of the fish that Tommy caught on the second day Estimate the snail population in were tagged? Annie’s garden. b) Estimate the total fish population in the lake. 40 × 6 = 240 fish in the lake. 5 16 × 5 = 80 snails What assumptions did you make? The snail population remained constant between each capture.

Capture-recapture 3. Dexter wants to estimate how 4. Eva catches some rabbits in a field, many buttons are in a jar. tags and releases them. He empties the jar out, marks 50 of The next day she captures 48 rabbits them, then mixes the buttons and 18 of them are tagged. returns them all to the jar. Eva estimates that the field has a He then takes 45 buttons out of the population of 120 rabbits. jar, 6 of them are marked. Use this information to work out how Show Dexter would use this many rabbits Eva initially caught and information to estimate the number tagged. 50 ÷ 2 × 15 = 375 of buttons in the jar. 6 120 ÷ 8 × 3 = 45 rabbits captured initially.