to determine the number of catfish in a pond, a game warden catches 131 catfish, tags them and throws them back into the pond. later, 20 catfish are caught, 10 of them are tagged. How many catfish would the game warden expect to be in the pond?
131/10 20/x
Assuming you meant
131/10 = 20/x
that would give you
131x = 20*10
x = 1.5
What can that mean? The ratios do not seem intuitive to me. I would have reasoned this way:
Of the sample caught, 10/20 were tagged. We can expect that the same fraction of the total population was tagged. In other words,
10/20 = 131/x
10x = 20*131
x = 262
To determine the number of catfish in the pond, we can use a method called the mark and recapture technique. This method assumes that the proportion of tagged catfish in the second sample (20 catfish caught) is representative of the proportion of tagged catfish in the entire population.
Let's break down the calculation step-by-step:
1. The initial number of tagged catfish that were released into the pond was 131.
2. In the second sample, 10 out of the 20 catfish caught were tagged.
Now, we can set up a proportion:
Number of tagged catfish in the initial sample / Total number of catfish in the pond = Number of tagged catfish in the second sample / Size of the second sample
131 / x = 10 / 20
Cross-multiplying the proportion:
[(131)(20)] = [(10)(x)]
2620 = 10x
Dividing both sides of the equation by 10:
2620 / 10 = x
262 = x
Therefore, the game warden would expect there to be approximately 262 catfish in the pond.