zlacker

I've always wondered if there's a probabilistic argument to show just how biased of policing there is by quantitating somehow the arrests made on a given subpopulation and somehow show how improbable it would be to randomly achieve a given arrest disparity to another subpopulation under the presumption of equal offending by those subpopulations. Is there any math to explore such a thing, sort of like flipping a quarter and hitting heads 5x in a row, that sort of thing.

To use a less charged example say I have three populations of fish, and all swallow coins in the same proportion as each other. In this universe sharks make up 10% of the fish population, sea-bass 30% and rockfish 60%. Exactly 5% of each fish type has a coin in their belly at any given time.

So if we have a world of 1000 fish, then we're talking 100 sharks, 300 sea-bass, and 600 rockfish. Of those 5 sharks, 15 sea-bass, and 30 rockfish have coins in their belly. To measure anything other than those counts of 5% per subpopulation, is there a way to measure how improbable that would be with random selection and subsampling and what not? Does this question even make sense and is well defined enough? My stats strengths aren't the keenest.