To determine the number of trout in a lake, conservationist catches 161 trout, tags them and throuws them back into the lake. Later, 39 trout are caught: 13 of them are tagged. How many trout would the conservationist expect to be in the lake?

Two hundred trout were tagged and then released into a pond. Later 60 trout were caught and examined, and 8 of the 60 trout were found to have tags. Estimate the number of trout in the pond.

To determine the number of trout in the lake, we can use the concept of marking and recapturing.

In this case, the conservationist caught 161 trout and tagged them. Later, 39 trout were caught, and out of those, 13 were tagged.

Based on the marking and recapturing method, we can set up a proportion:

(Number of tagged trout in the initial sample) / (Total number of trout in the lake) = (Number of tagged trout in the recaptured sample) / (Total number of trout in the recaptured sample)

Let's denote the total number of trout in the lake as 'x'.

From the given information:
Number of tagged trout in the initial sample = 161
Total number of trout in the recaptured sample = 39
Number of tagged trout in the recaptured sample = 13

Plugging in the values into the proportion:

161 / x = 13 / 39

Now, we can solve the proportion to determine the number of trout in the lake (x):

Cross-multiplying:
161 * 39 = 13 * x

6279 = 13x

Dividing by 13:
x = 6279 / 13

Calculating:
x ≈ 483

Therefore, the conservationist would expect there to be approximately 483 trout in the lake.

To determine the number of trout in the lake, we can use a method called the Lincoln-Petersen index.

The idea behind this method is that we can compare the proportion of tagged trout in the second catch to the proportion of tagged trout in the first catch. We can assume that the ratio of tagged trout to the total trout population is roughly the same in both catches.

Let's break down the information we have:

First catch:
- Number of trout caught and tagged = 161

Second catch:
- Number of trout caught = 39
- Number of tagged trout in the second catch = 13

Now, let's set up a proportion to find the estimated trout population:

(Number of tagged trout in the second catch) / (Number of trout in the second catch) = (Number of tagged trout in the first catch) / (Number of trout in the whole lake)

Using the given information:

13 / 39 = 161 / x

To solve for x, which represents the total trout population, we can cross-multiply and solve for x:

13x = 39 * 161
13x = 6319
x = 6319 / 13
x ≈ 485.31

Therefore, the estimated number of trout in the lake would be approximately 485 trout.

from the 13 tagged out of the 39 caught ...

13/39 = 1/3

so (1/3)x = 161
x = 483