A fishing cooperative wanted to get an estimate of how many specimens of a certain fish species, which have already reached a certain size, live in one of their ponds. (Hereafter, these will be referred to as suitable fish.) For this purpose, they marked 50 suitable fish from their daily catch and released them back into the water. The next day, in their catch from 3 different locations in the pond, they counted a total of 67, 94, and 43 suitable fish, respectively, and among these, 6, 10, and 3 were marked. How could they estimate the number of suitable fish after the second day's catch?
On the second day of fishing, out of 204 suitable fish, 19 were marked, which means they caught $38\%$ of all the marked fish. Assuming that the ratio of marked to total suitable fish before the second day of fishing was the same as what the catch showed, the 204 caught fish also represented $38\%$ of the total suitable fish population (i.e., the population before the catch). Thus, the morning population could be estimated at $204 \cdot 100 / 38 \approx 537$ individuals, and the number of suitable fish remaining in the lake was around 333.

Sipos László (Pannonhalma, Benedek-rendi g. II. o. t.)

Note. Many contestants, presumably with good intentions, provided separate estimates based on each fishing location (558, 470, 717, respectively), and then took the average (582). This is incorrect because the larger data sets from the second location are likely closer to the actual situation than those from the third location, so they should be given "greater weight." Consider how much more distorted the estimate would be if we added a location where only one fish was caught, whether that fish was marked or unmarked.

We merely mention that if the results from the 3 locations were taken into account with a weight proportional to the total number of fish caught at each, the result of the above simple calculation would be obtained.