People do think of conditional probabilities that way, one just has to be careful not to conflate with p(IF event1 THEN event2), which is a probability of a disjunction, and quite different from p(event2 | event1). Conditioning is kind of weird, Simpsons paradox is a paradox because we are really bad at processing what conditioning actually means.
People do think of conditional probabilities that way, one just has to be careful not to conflate with p(IF event1 THEN event2), which is a probability of a disjunction, and quite different from p(event2 | event1). Conditioning is kind of weird, Simpsons paradox is a paradox because we are really bad at processing what conditioning actually means.