Probability problem (came in TIFR)

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SUMMARY

The marine biologist estimated the fish population in a lake using the capture-recapture method. Initially, he caught and marked 30 fish. Upon recapturing 40 fish the next day, he found 2 of them were marked. By setting the fractions of marked fish equal (30/P = 2/40), he calculated the total fish population, concluding that the approximate number of fish in the lake is 600.

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  • Understanding of capture-recapture methodology
  • Basic knowledge of probability and fractions
  • Familiarity with population estimation techniques
  • Ability to solve simple algebraic equations
NEXT STEPS
  • Research the Lincoln-Petersen estimator for population studies
  • Learn about the assumptions and limitations of capture-recapture methods
  • Explore advanced statistical methods for wildlife population estimation
  • Investigate the impact of marking techniques on population studies
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Marine biologists, ecologists, statisticians, and anyone involved in wildlife population studies will benefit from this discussion.

cgchayan
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A marine biologist wanted to estimate the number of fish in a large lake. He threw a net and found 30 fish in the net. He marked all these fish and released them into the lake. The next morning he again threw the net and this time caught 40 fish, of which 2 were marked. The approximate number of fish in the lake is :
a)600
b)1200
c)68
d)800
e)120
 
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The typical (introductory) way to attach this is to make this assumption:

1) let P denote the fish population
2) 30/P is the fraction of fish population marked with the first catch
3) 2/40 is the fraction of the second catch found to be marked

The assumption is that the two fractions are the same; solving for P gives the approximate population.
 

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