to determine the number of trout in a lake a conservationist catches 191 trout, tags them and throws them back into the lake. Later, 36 trout are caught; 12 of them are tagged. How many trout would the conservationist expect to be in the lake?
1/3 of the trout caught have been tagged.
(1/3) * 191 = ?
To estimate the number of trout in the lake, we can use a method called the mark and recapture technique.
This technique assumes that the proportion of tagged trout in the second sample is the same as the proportion of tagged trout in the initial sample. We can use this assumption to calculate the estimated population size of the trout in the lake.
Let's break down the information provided:
1. The conservationist catches and tags 191 trout in the lake.
2. Later, 36 trout are caught in a subsequent sample.
3. Out of the 36 trout caught, 12 of them are tagged.
Now, we can set up a proportion to find the estimated population size (N) of the trout in the lake:
(tagged fish in initial sample) / (total fish in initial sample) = (tagged fish in subsequent sample) / (total fish in subsequent sample)
Using the numbers from the information given:
(191 tagged fish) / (total fish in initial sample) = (12 tagged fish) / (36 total fish)
To find the estimated population size (N), we can cross-multiply and solve for N:
12(total fish in initial sample) = 191(36)
(total fish in initial sample) = (191(36)) / 12
(total fish in initial sample) = 5736 / 12
(total fish in initial sample) = 478
Therefore, the conservationist would expect there to be approximately 478 trout in the lake.