174","questionNumber":"2","questionType":"LA","specification":"Carlos wants to find an estimate for the number of ants in a colony.\n\nHe catches 60 ants from the colony and marks each one with a dye. He then returns the ants to the colony.\n\nA week later, Carlos catches another 60 ants. 8 of these ants are marked with the dye.","difficulty":1,"difficultyBand":"medium","totalMarks":3,"sourceTitle":"Capture Recapture","calculatorUse":null,"isCalculation":true,"parts":[{"id":"62a3cc84-4f11-43d0-8e69-59af53d10e5b","label":"","content":"Work out an estimate for the number of ants in the colony.\n\nWrite down an assumption you have made.","markscheme":"- Sets up ratio: $\\frac{60}{x} = \\frac{8}{60}$ M1\n- Calculates estimate: $60 \\times 7.5 = 450$ A1\n- States assumption: e.g., the dye stayed on all of the ants. B1","marks":3,"order":0,"markingRubric":{"totalMarks":3,"points":[{"id":"p1","marks":1,"description":"Sets up a correct proportion, e.g., $\\frac{60}{x} = \\frac{8}{60}$.","code":"M"},{"id":"p2","marks":1,"description":"Correct estimate of 450.","code":"A"},{"id":"p3","marks":1,"description":"States a valid assumption regarding the marks or the population.","code":"B"}],"finalAnswers":["450"],"generatedAt":"2026-05-06T15:23:48.190Z","modelVersion":"gemini-3-flash-preview"},"tableImages":[],"explanation":{"methods":[{"id":"capture_recapture","label":"Capture–recapture","steps":[{"type":"hyper_latex","block":{"nodes":[{"latex":"\\text{estimated marked proportion}=\\frac{60}{x}"},{"latex":"\\frac{60}{x}=\\frac{8}{60}"}]},"order":1,"title":"Form the ratio","description":"Let x be the total number of ants in the colony. Estimate the marked proportion in the colony using the marked proportion in the second catch. Forming this proportion earns M1."},{"type":"hyper_latex","block":{"nodes":[{"latex":"\\frac{60}{x}=\\frac{8}{60}"},{"latex":"x=60\\times\\frac{60}{8}"},{"latex":"x=60\\times 7.5"},{"latex":"x=450"}]},"order":2,"title":"Calculate the estimate","description":"Rearrange the proportion to find the total colony size. So the estimated colony size is 450 ants. This earns A1."},{"type":"text","order":3,"title":"State an assumption","content":"Assume that the dye stayed on all the marked ants during the week. This earns B1."}]}],"generatedAt":"2026-07-20T16:23:35.712Z","modelVersion":"gpt-5.6-sol","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":{"percent":65},"walkthroughVideo":null},{"id":"0310a90f-ffe1-4a8f-bdcc-93495e529b48","revisionId":"79d27630-cdfe-4c44-a15e-3c2304b2d1f2","questionNumber":"3","questionType":"LA","specification":"Beth wants to estimate the number of frogs in a lake. She catches a sample of 80 frogs, marks them and puts them back in the lake. Later that day, in a second sample of 80 frogs, she finds that 10 of them are marked.","difficulty":1,"difficultyBand":"medium","totalMarks":3,"sourceTitle":"Capture Recapture","calculatorUse":null,"isCalculation":true,"parts":[{"id":"b4f25725-d0f2-4581-9b48-2ead79c250c9","label":"a","content":"Work out an estimate for the number of frogs in the lake.","markscheme":"- Sets up ratio: $\\frac{80}{x} = \\frac{10}{80}$ M1\n- Calculates $80 \\times 8 = 640$ A1","marks":2,"order":0,"markingRubric":{"totalMarks":2,"points":[{"id":"p1","marks":1,"description":"Correct method to find estimate, e.g., $\\frac{80 \\times 80}{10}$.","code":"M"},{"id":"p2","marks":1,"description":"Final answer of 640.","code":"A"}],"finalAnswers":["640"],"generatedAt":"2026-05-06T15:23:48.190Z","modelVersion":"gemini-3-flash-preview"},"tableImages":[],"explanation":{"methods":[{"id":"capture_recapture","label":"Capture–recapture","steps":[{"type":"text","order":0,"title":"Match proportions","content":"The proportion of marked frogs in the whole lake is estimated using the proportion of marked frogs in the second sample. This is the capture–recapture method, so the unknown total is represented by $x$.","highlights":[{"text":"estimate the number of frogs in a lake

Capture Recapture

Question 2

Capture Recapture Questions

Capture Recapture

Question 2

Capture Recapture Questions