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Capture-recapture estimates

Solve the first problem 5 problems

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1. Estimating frog population by recapture ●○○○○ 10 ptsOne day, 45 frogs were captured from a pond, marked and then returned to the pond. The next day, 40 frogs were observed in the pond, of which 10 had been marked the previous day. Assuming the marked frogs are equally distributed among all the frogs in the pond, what is the best estimate of the number of frogs living in the pond?
2. Estimating fish population by recapture ●○○○○ 10 ptsManagement staff caught 30 fish from a pond, marked them, and released them back into the pond. 10 days later, they caught 50 fish from the pond, of which 2 were marked. Assume the marked fish have mixed evenly through the pond, so the proportion marked in the second catch estimates the proportion marked in the whole pond. Based on this data, estimate the total number of fish in the pond.
3. Estimating fish population by capture-recapture ●○○○○ 10 ptsTo estimate the number of fish in a pond, $100$ fish were caught, tagged, and then released back into the pond. After some time, when the tagged fish had mixed completely with the rest of the fish, another $200$ fish were caught. If $10$ of them were tagged, estimate the total number of fish in the pond.
4. Fish population by tag and recapture ●●○○○ 20 ptsA biologist wants to estimate the number of fish in a lake. On May 1 she catches a random sample of 60 fish, tags them, and releases them. On September 1 she catches a random sample of 70 fish and finds that 3 of them are tagged. To estimate the number of fish in the lake on May 1, she assumes that 25% of the May 1 fish are no longer in the lake on September 1 (because of death and emigration), that 40% of the fish in the lake on September 1 were not in the lake on May 1 (because of births and immigration), and that the tagged and untagged fish in the September 1 sample are representative of the whole population. What number does she calculate for the number of fish in the lake on May 1?

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