Two editors, Ed and his boss Ada have just finished the proof-reading of a new book prior to its publication.
Working independently, Ed detected 25 errors and Ada ended up only with 19.
Provide your estimate (assume what you may) regarding the quantity of errors still remaining after their inspection.
Spotty Editing is a similar problem to this one, except this time we don't know the total number of errors found.
Let E be the total number of errors in the book and let D be the total number of errors found by both Ada and Ed (this will be between 25 and 44).
Then applying the solution from Spotty Editing yields an initial equation of: E - D = E * (E-19)/E * (E-25)/E
This simplifies to E = 475/(44-D).
If many of the errors found by Ed were also found by Ada (D is close to or exactly 25) then the total number of errors is small. If D=25 then E is 25 implying they found all errors. A little bigger D=27 implies E=28 so then they only missed one error.
But if the errors found by Ed and Ada are largely different then there could be a huge number of errors still around. If D=41 then E=158 which means that they found slighty more than a quarter of the errors. Worst case scenario is Ed and Ada found all different errors with D=44. Then E diverges to infinity and for all we know the entire book could be nothing but errors.
We do need some additional info to make a more substantive claim about the errors that may actually be in the book. Obviously having a value for D would work.
Just a number for the quantity of things checked may offer an alternate approach. 25 errors in a short book of 10000 words is going to be different from 25 errors in a typical novel of 60000-90000 words.
Thoughts
