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You catch, tag, and release 50 fish back into a pond. Then, you catch 25 more fish, 5 of which are tagged. What is the best estimate of the number of fish in the pond?100 fish250 fish400 fish625 fish

Question

You catch, tag, and release 50 fish back into a pond. Then, you catch 25 more fish, 5 of which are tagged. What is the best estimate of the number of fish in the pond?100 fish250 fish400 fish625 fish

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Solution

This is a classic example of a mark and recapture method used in ecology to estimate population sizes. Here's how you can solve it:

  1. First, you tagged 50 fish and released them back into the pond.
  2. Then, you caught 25 fish, out of which 5 were tagged.
  3. This means that the proportion of tagged fish in your second sample (5 out of 25, or 1/5) should be roughly the same as the proportion of tagged fish in the entire pond (50 out of the total population).
  4. You can set up the equation 50/X = 1/5, where X is the total population of the fish in the pond.
  5. Solving for X gives you X = 50 * 5 = 250.

So, the best estimate for the number of fish in the pond is 250 fish.

This problem has been solved

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