Idiots
We know they test once a week. Wait sober until they test, and drink until the weekend. Probability of being caught 0!
Alternatively, it's almost certain that the boss will have been seduced by sales spiel into buying the latest fanciest internet connected alcohol testing machine. Even the greenest PFY should be able to insert the 'if dept = IT then alcohol = random number between totally sober and reasonably sober' into the code. Or maybe the simpler 'if dept = HR then alcohol = embarrassingly pissed'
And pedantically, assuming that the employee's drinking is reasonably spread your green and red balls are a bit skewed - (I think - of course last night's bender might be clouding my judgement), because while in week 1 you may have 248 red 12 green, but week 2 we should be calculating 243 red 11.75 green, - the odds of being caught aren't changing any more than the odds of throwing a coin change? Your numbers assume that if I was sober on test 1 the chances of me being sober on test 2 are slightly less, effectively assuming that there are still 12 drunk balls, but now 247 sober ones.
I think it was just a poorly labelled table and the best way of thinking about it is there's a 12/260 chance that I'm drunk on a given day and a 52/260 chance that I will be tested on a given day
so for a given day the probability of getting away with it = 0.04 * 0.2 = 0.009 as it was in the table
They just forgot that I come to work 260 days a year (for which I'd need to be on something) so
260*0.009 = 2.4, a 240% chance of being busted. That empirically feels right, If I do something where i have a 20% chance of being caught 12 times in a row, I'm going to get caught.
Biting the hand that feeds IT
