Did I really let almost a month elapse without posting? Must be because my life is so wild and exciting. Um, yeah.
Here's a question that's been occupying me for a while -- non-mathematicians' perception of probability. What does a man on the street mean when he says a coin has a 50% chance of landing on heads?
The most likely interpretation is frequentist: if you flip the coin a whole lot of times, you'll see heads about half the time, on average. (How many times is a lot? What does on average mean here? Read my thesis -- at least the section on the Law of Large Numbers.)
But what about one-time events? What does it mean that there's a 30% chance of rain tomorrow? (Tomorrow will only happen once, so any talk of averages is meaningless.) Heck, what does the meteorologist mean by that probability?
Cosma helped me resolve the latter quite satisfactorily in private correspondence (so satisfactorily, in fact, that I feel dumb ever having asked the question). But I turn to the readers:
1. can you make rigorous mathematical sense out of the meteorologist's 30% chance of rain prediction?
2. can you ask your non-mathematician friends what that prediction means to them?