10. To estimate the number of fish in a pond, a researcher catches 25 fish randomly,
marks them with yellow paint and then puts them back in the pond. The researcher
comes back the next day and again catches 25 fish randomly and finds that 5 of them
have yellow paint. Estimate the total number of fish in the pond?
a. 25 fish
b. 125 fish
c. 625 fish
d. 250 fish
The total number of fish in the pond is estimated at 125 (option b).
This problem uses the mark-recapture method, also known as the Lincoln-Petersen estimator, a standard ecological sampling technique to approximate population sizes in closed systems like ponds. First catch involves marking 25 fish with yellow paint and releasing them, assuming random mixing. Second catch of 25 fish yields 5 marked ones, so the proportion of marked fish in the sample (5/25 = 0.2) equals the proportion in the total population (25/N, where N is total fish).
The formula derives from this equality: (marked in sample / sample size) = (marked total / population total). Thus, N = (marked × recaptured) / marked in recapture = (25 × 25) / 5 = 625 / 5 = 125 fish. This assumes no births, deaths, migration, or marking effects during the interval, conditions typical for such exam scenarios.
Option Analysis
-
a. 25 fish: Assumes sample size equals population, ignoring marked proportion (5/25=20% marked implies much larger total). Far too low.
-
b. 125 fish: Matches Lincoln-Petersen calculation exactly (25×25)/5=125, correct under ideal assumptions.
-
c. 625 fish: Equals marked × recaptured without dividing by recaptured marked, a common misapplication missing proportion adjustment.
-
d. 250 fish: Might arise from (25×25)/2.5 or doubling sample, inconsistent with data (would imply only 2.5 marked in sample).
Estimate total fish pond mark recapture 25 fish 5 yellow problems appear in CSIR NET Life Sciences quantitative aptitude sections, testing population estimation basics vital for ecology and wildlife biology. Master the formula N=(M×C)/R where M=marked, C=caught second, R=recaptured marked for quick solves, eliminating distractors via proportion checks.
