The answer is ((A-C)(B-C))/C

While it is not possible to find an exact answer, it is possible to find the best approximation. This is the method that many biologists use to estimate the population of a given animal in a given area. In fact, the animal analogy is very apt.

Imagine that a biologist randomly catches A animals and puts tags on all of them. Then, the biologist releases all of them. Assuming no animals breed, die, enter, or leave, the population will remain constant. Later, the biologist randomly catches B animals. This simulates the fact that John and David worked independently, since both catches were completely random and came from the same set. The biologist notices that of the B animals that he has just caught, C of them have the tags that he put on last time. The ratio of B to C is equal to the ratio of the total animal population (T) to A; in short, B/C=T/A. Ergo, T=(AB)/C. Normally, the biologist would be done here, but we have to do a little more manipulation.

Let's come back to the original problem: (AB)/C is the best estimate for the total number of errors. Between John and David, they caught A+B-C mistakes. The number of mistakes they did not catch would obviously be (AB)/C-(A+B-C). We could finish here.

However, further mathematical manipulation resolves to (AB-AC-BC+CC)/C. By factoring, we get (A(B-C)-C(B-C))/C, which factors again to our elegant answer, ((A-C)(B-C))/C.

所有跟帖： 

• 回复：The answer is ((A-C)(B-C))/C -jinjing- ♀ (74 bytes) () 05/18/2010 postreply 20:51:10

• Wonderful,I learn something new from you. Thanks! -皆兄弟也- ♂ (0 bytes) () 05/18/2010 postreply 21:23:54

• 你不是 -AnaZhang- ♀ (71 bytes) () 05/19/2010 postreply 11:46:22

• I said what I really did. -皆兄弟也- ♂ (0 bytes) () 05/19/2010 postreply 13:08:46

• 其实这么理解就行了 -twfx- ♂ (77 bytes) () 05/20/2010 postreply 09:50:09

• 这个也对，而且更简洁。 -不明则问- ♂ (0 bytes) () 06/02/2010 postreply 09:46:12

• 对！ -不明则问- ♂ (42 bytes) () 06/02/2010 postreply 09:45:44