A government agency wants to estimate the number of fish in a lake. People from the agency catch 100 fish, tag them, and put them back in the lake. A short while later, they catch 100 fish and find that 10 have been tagged. Think of this second batch as a random sample of all of the fish in the lake. Based on this sample, what is your estimate of the fraction of the fish in the lake that are tagged? Because you know that 100 fish are tagged, what is your estimate of the total number of fish in the lake?