I went through the same thing. If P(A|B) is extremely high, and A is otherwise rare, then the event where B happens is more likely, right?!
But if A happens given B, A still happens. A remains a subset of A intersect B. I had this conditional probability thought and almost discounted it like “oh this fallacy and blog post assumes independent events”. Though this is not the case!
I went through the same thing. If P(A|B) is extremely high, and A is otherwise rare, then the event where B happens is more likely, right?!
But if A happens given B, A still happens. A remains a subset of A intersect B. I had this conditional probability thought and almost discounted it like “oh this fallacy and blog post assumes independent events”. Though this is not the case!