You want to estimate how many fish there are in a pond. Suppose you capture 290 fish, tag them, and throw them back into the pond. After a couple of days, you go back to the pond and capture 580 fish, of which 29 are tagged.

To estimate the number of fish in the pond, we can use a technique called mark and recapture. The basic idea is that we can use the ratio of tagged fish to the total number of fish in the second sample to estimate the total population. Let's denote the total number of fish in the pond as "N." According to the mark and recapture method, we can set up a proportion: (Number of tagged fish in the first sample) / (Total number of fish in the pond) = (Number of tagged fish in the second sample) / (Total number of fish in the second sample) Plugging in the given information, we have: 290 / N = 29 / 580 To solve for N, we can cross-multiply and solve the equation: 29N = 290 * 580 N = (290 * 580) / 29 N ≈ 5,800 Therefore, the estimated number of fish in the pond is approximately 5,800.