[ad_hominem]

> it may be true that most criminals in an area are of a certain race; that says nothing about the likelihood of a single person of that race being a criminal

Huh? If 10% of purple people in an area have been incarcerated, and you select one individual from the purple people population of that area at random, the odds are 10% the individual you selected will have been incarcerated. That's fundamental to how sampling works.

[schrodinger]

The situation isn’t that 10% of purple have been incarcerated; if it was, you’d be correct.

Instead, the situation is that 90% of those incarcerated are purple. You can’t draw any meaningful conclusions from that without knowing the number that you were referring to: what percentage of purple people that makes up.

[imgabe]

You are flipping around the percentages. Parent says "10% of incarcerated people are purple". This does not imply that "10% of purple people are incarcerated".

[tnzn]

Except that's not what happens.

[fludlight]

Random sampling doesn't work well with small sample sizes.