The barbarians running rampant in the Ethereal Land are known for their sometimes-violent dislike of academic mathematics. The present author appreciates this and recognizes that this article on statistical probability may cause pain and suffering if read. Nevertheless the reading of the same is recommended, because it is making an important point: that statistics are useless if you are not measuring precisely the right event.

To generalize, the fallacy presented here is the assumption of causual relationship between physically unrelated events. These hypothetical word-problem test questions could have been constructed in a way to actually make the probabilities compound, but they weren’t; the facts as stated do not warrant the assumption of relationship that the “right” answer supposes.

To apply, when people make unwarranted assumptions of relationship, they can then make further proofs using statistics (or logic) and then champion it as scientifically proved and incontrovertible. But statistics and logic are processes; they require inputs; all of the inputs affect the outcomes; and not all of the inputs are always confessed openly. Just because someone uses more complicated science than you understand does not mean that they used the science correctly or are right in their results.