Estimate how many fish there are in the lake. Catch 100 fish for marking, and then put it back. After a period of time, after the marked fish and the fish were completely mixed together, 200 fish were caught and 20 marked fish were found, so the number of fish in the lake was about 20. Please explain why.

So there are fish:100/[20/200] =1000.

20 of the 200 catches were marked, accounting for 20/200 =110.

Then the fish marked with 100 also accounts for110, so the total number of fish is:100/[10] =1000.