To estimate the number of fish in a small lake researchers c

To estimate the number of fish in a small lake, researchers caught 200 fish, tagged them, and returned them to the lake. The next day they caught 100 fish. Of those caught, 25 had a tage, What would be a good guess for the total number of fish in the lake? If there were 800 in the lake and the same procedure were followed, what is the probability that 25 of the 100 fish in the second catch would have been tagged?

Solution

there are total 800 fish in a lake

out of which 200 were tagged

probability of tagged fish = 200/800 = .25

applying binomial distribution

x = 25

n = 100

p = .25

q = .75

p(25) = 100c25 * .25^25*.75^75

on solving we get

p(25) = .0918