Re: Am I missing something? (I am most definately not a mathmatician)
I'm surprised it took till page 3 for me to find someone else saying this, specifically, how do you know (apart from on day 1) how many red balls are in there?
Every day, someone takes out 1 ball, but you don't know what colour it is. so there is a possibility that after say, 15 days, all 12 red have been taken out, but because they were removed on non test days, you have no idea. As the tester, every day (whether you are testing or not) there are between 0-12 red balls in the bag.
As others have said, there is a chance that people are coming in drunk on consecutive days, so that could be two or three reds in a row, which would increase the immediate chance of getting caught, but in the long term it would decrease it (which i guess balances out?)
i think I'm getting carried away here because it's Friday morning and I'm full of caffeine, but, with the 'balls test' (in this case) surely the correct way to conduct it, is for two people to be involved, one (the 'drunk', chooses a ball from the bag, and keeps it to them selves, unless the other person (the 'tester') asks them what it is, repeat until either the bag is empty or the 'drunk' gets caught.