pond with 50 fish is endangered as some of the fish is attacked by parasites. In an attempt to find out how much of the fish is attacked to persons A and B check 10 fish each for the parasite. They do this in different ways, however:
Person A catches a fish, checks for parasites, and lets it back into the pond. This he does 10 times.
Person B catches 10 fish, checks all of them, and lets them back into the pond.
Let X be the number of infected fish person A registeres, and Y be the number of infected fish person B registres.
Which distribution does X and Y get?
Now, person B should be able to make the best estimate, as person A risks counting any given fish more than once. Still, I don't know if it will give them different distributions, or even which kinds. Any help?