Correct me if I’m wrong, but isn’t the probability of a year being a leap year approximately 25%, completely independent of what month it is? (This seems like one of those unintuitive-but-correct probability puzzles...)
For all intents and purposes, yes. Well, for nearly all intents and purposes, since there is in fact a very slight difference:
Imagine the year only had 2 months, PraiseKawoombaMonth, and KawoombaPraiseMonth, each of those having 30 days. However, every other year the first month gets cut to 1 day to compensate for some unfortunate accident involving shortening the orbital period. Still, for any given year the probability of being a leap year is 50%.
Now you get woken from cryopreservation (high demand for fresh slaves) and, asking what time it is, only get told it’s PraiseKawoombaMonth (yay!). This is evidence that strongly informs you that you are probably in one of the equi-month years, since otherwise it would be very unlikely for you to find yourself in PraiseKawoombaMonth.
Snap, back to reality: Same thing if you’re told it’s August, the chance of being in August at any given time is lower in a leap year, since the fraction of August per year is lower. There’s just more February to go around!
Sorry for the quality of the explanation. It’s the only way I can explain things to my kids.
Correct me if I’m wrong, but isn’t the probability of a year being a leap year approximately 25%, completely independent of what month it is? (This seems like one of those unintuitive-but-correct probability puzzles...)
For all intents and purposes, yes. Well, for nearly all intents and purposes, since there is in fact a very slight difference:
Imagine the year only had 2 months, PraiseKawoombaMonth, and KawoombaPraiseMonth, each of those having 30 days. However, every other year the first month gets cut to 1 day to compensate for some unfortunate accident involving shortening the orbital period. Still, for any given year the probability of being a leap year is 50%.
Now you get woken from cryopreservation (high demand for fresh slaves) and, asking what time it is, only get told it’s PraiseKawoombaMonth (yay!). This is evidence that strongly informs you that you are probably in one of the equi-month years, since otherwise it would be very unlikely for you to find yourself in PraiseKawoombaMonth.
Snap, back to reality: Same thing if you’re told it’s August, the chance of being in August at any given time is lower in a leap year, since the fraction of August per year is lower. There’s just more February to go around!
Sorry for the quality of the explanation. It’s the only way I can explain things to my kids.