Probability problem (came in TIFR)

[cgchayan]

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

 

[statdad]

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.