Well, because it does.

Let's say we have a group of 1000 animals: 900 rabbits and 100 foxes.

We also know that there are about 10 crimes happening every year and for every crime there's 50% chance of it being committed by a fox.

Then according to Bayes' formula:

P(fox is a criminal) = P(criminal is a fox) * P(animal is a criminal) / P(animal is a fox) = 0.5 * 0.01/0.1 = 0.05 = 5% chance for every given fox to be a criminal.

For every given rabbit the same formula gives 0.5 * 0.01/0.9 which is roughly 0.6%.

Not every animal in Australia is a kangaroo.

Nevertheless, if you want to find a kangaroo in a wild, heading to Australia, would probably be your best bet.

Sure, but if you're looking for kangaroos because of an incorrect belief that they're mostly responsible for something, and it's actually perpetrated more by mountain lions, you might actually be on the wrong continent.

Incels have killed more people than Islamic extremists in the US in the last decade.

Re the systematic racist bias in 4. - since you postulate a world in which 100% of terrorists are muslims, why would anyone non-muslim ever be investigated for terrorism? (whether with 'gusto' or not)

Because point 4 is about non-terrorist charges. Pretty much what we find with the black population being biased with charges of drug possession. If searches are applied to blacks 10x as often relative to whites, then if neither is more likely to possess marijuana you'll come up with statistics which say 10x as many blacks illegally possess marijuana than whites. When instead one needs to say what percentage of those searched are in possession

> if neither is more likely to possess marijuana

Research says drug usage rate is similar for black and white people in the US, but prosecution and conviction rates are not[1]

1. http://www.hamiltonproject.org/charts/rates_of_drug_use_and_...

No, point 4 was about the fact that somehow it is racist to prosecute people of type X for crimes they commit if those crimes are discovered because of an investigation into a different type of crime (which only type X people commit) - the alternative being to give them a free pass, I assume? The premise doesn't hold water anyway, since even in this hypothetical world where only type X are terrorists, I assume terrorism is still a rare event? So, the extra crimes discovered in the course of terrorism investigations into type X suspects will be dwarfed by the investigations into normal crimes in the whole population during the course of normal every day police work.

// Assuming the police are not incompetent, of course, which may not hold in your hypothetical world where they investigate non type X people for terrorism even though they commit zero percent of terrorist attacks - probably out of some misguided diversity quota or affirmative action policy, I assume? ;)

This is conflating an ideology with an intrinsic quality, doesn't this imply your projected irrational bias?

> In order to find 0.001% of terrorists you will have to pick through 999 innocent muslims.

99,999, not 999 innocents and 1:100,000, not 1:1000 (making your point stronger)

> that’d say nothing about the likelihood

> There's a 0.001% chance of finding a terrorist per random sampling.