Congrats on applying Bayes; unfortunately, you applied it to the wrong numbers.
The key point is that “Question 3: Bayes” is describing a new village, with demographics slightly different to the village in the first half of your post. You grandfathered in the 0.2 from there, when the equivalent number in Village Two is 0.16 (P(Cat) = P(Witch with Cat) + P(Muggle with Cat) = 0.1*0.7 + 0.9*0.1 = 0.07 + 0.09 = 0.16), for a final answer of 43.75%.
(The meta-lesson here is not to trust LLMs to give you info you can’t personally verify, and especially not to trust them to check anything.)
ETA: Also, good on you for posting this. I think LW needs more numbery posts, more 101-level posts, and more falsifiable posts; a numbery 101-level falsifiable post gets a gold star (even if it ends up falsified).
Congrats on applying Bayes; unfortunately, you applied it to the wrong numbers.
The key point is that “Question 3: Bayes” is describing a new village, with demographics slightly different to the village in the first half of your post. You grandfathered in the 0.2 from there, when the equivalent number in Village Two is 0.16 (P(Cat) = P(Witch with Cat) + P(Muggle with Cat) = 0.1*0.7 + 0.9*0.1 = 0.07 + 0.09 = 0.16), for a final answer of 43.75%.
(The meta-lesson here is not to trust LLMs to give you info you can’t personally verify, and especially not to trust them to check anything.)
ETA: Also, good on you for posting this. I think LW needs more numbery posts, more 101-level posts, and more falsifiable posts; a numbery 101-level falsifiable post gets a gold star (even if it ends up falsified).
Thank you for your help and excellent comment!