To estimate the number of bass in a lake, a biologist catches and tags 24 bass. Several weeks later, the biologist catches a new sample of 44 bass and finds that 2 are tagged.

Question

To estimate the number of bass in a lake, a biologist catches and tags 24 bass. Several weeks later, the biologist catches a new sample of 44 bass and finds that 2 are tagged. How many bass are estimated to be in the lake?

Answer 1

We can assume that the ratio "tagged to total" is the same for those fishes caught than for those in the pound:

tagged caught : total caught = tagged in the pound : total in the pound

tagged caught / total caught = tagged in the pound / total in the pound

In this case:

tagged caught = 2

total caught = 44

tagged in the pound = 24

total in the pound = x

2 / 44 = 24 / x

Solving for x:

x = (44 * 24) / 2

x= 1056 / 2

x = 528

There is an estimate of 528 fishes in the pound.

Answer 2

Using the Chapman-Petersen equation,

Estimate = (M+1)(C+1)/(R+1)

M = First sample size

C = Second sample size

R = number of recaptures

For this case,

Estimate = (24+1)(44+1)/(2+1) = 25(45)/3 = 375