A fish and game warden captures and tags 66 deer in a local forest. A month later he captures 100 deer and finds that 17 of them are tagged. Estimate the actual number of deer in the forest
One possible method to estimate the actual number of deer in the forest is to use a proportion or ratio based on the ratio of tagged deer to total deer in the two samples. Assuming that the tagged deer are representative of the entire population and that the warden's capture methods and timing did not significantly affect the composition of the samples, we can set up the following proportion:
tagged deer in first sample / total deer in first sample = tagged deer in second sample / total deer in second sample
or
66 / x = 17 / 100
where x is the actual number of deer in the forest. We can solve for x by cross-multiplying and simplifying:
66 * 100 = 17 * x
x = 66 * 100 / 17
x ≈ 388 (rounded to the nearest whole number)
Therefore, the estimated actual number of deer in the forest is about 388.