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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.