I need another brain on this one to generalize a specific case, and I'm having some difficulty putting it into words.
We mark fish in a variety of ways. Normally, there is one or two marks, but there could be more. The quality of each type of mark is independent of any other type of mark, but can be categorized as good or bad. Therefore, if you have 10,000 fish marked with marks A and B, then it might be that 90% of the fish have mark A (90% good, 10% bad for that mark), while 99% of the fish have mark B (99% good, 1% bad for that mark). I believe this means that of the 10,000, there will be 8910 with both A and B, 910 will have just B, 90 will have just A, and 90 will have neither. I think that's right, anyways.
I need to categorize these as good, partial, or bad, so I would make it to be 8910 good, 1000 partial, and 90 bad.
What I want to do is generalize this for N marks. So, given different rates of good and bad for each mark, what is the number that has all the marks, and what is the number that has none of the marks. The rest ends up as partial. Is there any calculation that simplifies this? I don't believe that N can go above 5, and probably won't go above 3, so working it out for each would be possible, but I'd rather generalize for all N.
We mark fish in a variety of ways. Normally, there is one or two marks, but there could be more. The quality of each type of mark is independent of any other type of mark, but can be categorized as good or bad. Therefore, if you have 10,000 fish marked with marks A and B, then it might be that 90% of the fish have mark A (90% good, 10% bad for that mark), while 99% of the fish have mark B (99% good, 1% bad for that mark). I believe this means that of the 10,000, there will be 8910 with both A and B, 910 will have just B, 90 will have just A, and 90 will have neither. I think that's right, anyways.
I need to categorize these as good, partial, or bad, so I would make it to be 8910 good, 1000 partial, and 90 bad.
What I want to do is generalize this for N marks. So, given different rates of good and bad for each mark, what is the number that has all the marks, and what is the number that has none of the marks. The rest ends up as partial. Is there any calculation that simplifies this? I don't believe that N can go above 5, and probably won't go above 3, so working it out for each would be possible, but I'd rather generalize for all N.