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.
(tagged/total) = (8/60)= 200 / x
2/15 = 200/x
1/15 = 100/x
x = 1500
To estimate the number of trout in the pond, we can use a method called mark and recapture. This method assumes that the ratio of tagged trout to untagged trout in the recaptured sample is similar to the ratio in the entire population.
Let's break down the information given:
- 200 trout were initially tagged and released into the pond.
- Later, 60 trout were caught and examined.
- Out of these 60 trout, 8 were found to have tags.
Using this information, we can set up a proportion to estimate the total number of trout in the pond:
(Tagged trout in the population) / (Total trout in the population) = (Tagged trout in the recaptured sample) / (Total trout in the recaptured sample)
The number of tagged trout in the population is known (200), the number of tagged trout in the recaptured sample is known (8), and the total number of trout in the recaptured sample is known (60). However, we need to find the total number of trout in the population.
Let's set up the proportion and solve for the missing value:
(200) / (Total trout in the population) = (8) / (60)
Cross-multiplying the equation, we get:
8 * (Total trout in the population) = 200 * 60
Simplifying further:
8 * (Total trout in the population) = 12000
Now, we can solve for the total number of trout in the population:
Total trout in the population = 12000 / 8 = 1500
Therefore, the estimated number of trout in the pond is 1500.