The more general lesson here is that when given the conditional “If A then B” [in this case, if males are assigned to Veblen South then males are assigned to Wisteria North] there is one good inference (the contrapositive) and two bad inferences.

Here is the good inference: If not B then not A.

Here is the first bad inference: If not A then not B.

Here is the second bad inference: If B then A.

So it sounds like you are asking for additional clarification as to why the second bad inference is a bad inference. Here’s why: Imagine that ‘A’ stands for ‘Danny’s head gets chopped off”, and ‘B’ stands for ‘Danny is dead’. If Danny’s head gets chopped off, then Danny is dead. But there are lots of possible ways for Danny to die. So if we are given the conditional that If Danny’s head gets chopped off, then Danny is dead, and then we are told that Danny is dead, we cannot infer that Danny’s head got chopped off- maybe Danny was poisoned? Had a heart attack? Who knows? All we know is that *if *Danny’s head got chopped off, then Danny is dead, which also means that if Danny is not dead, then Danny’s head did not get chopped off (this is the contrapositive). If Danny is dead it is of course *possible *that Danny’s head got chopped off, but it isn’t *necessarily *the case.

Back to the game: The conditional tells us that If males are assigned to Veblen South, then males are assigned to Wisteria North. So, if males are assigned to Wisteria North, it is of course *possible *that males are assigned to Veblen South, but it isn’t *necessarily *the case.