I'm taking a basic Stats course right now - I've taken it before, but it's been too long, and I could use the refresher as well. Nothing new here, but in reading the textbook, something jumped out at me that sort of bugged me. It's this.

0 <= P(x) <= 1

Or, the probability of an outcome is between the values of zero and one, inclusive. Also, if you sum all possible outcomes, the cumulative probability should equal one exactly. For example, the probability of a rolled six-sided die coming up as 1 is 1/6, or ~16.67%. likewise, summing the probabilities of all possible outcomes is 6/6, or 100%

This bugs me, because it's not true. A six sided die can land on its edge - I've seen this happen. Maybe it'll explode mid-air. Maybe it'll just disappear. These examples are all infinitesimally probable (increasingly so), but we're talking about theoretical probability here, so we have to be exact. Just like in calculus, where lim(x) != x, in probability, just because the probability approaches 1 (or 0) doesn't mean it ever actually gets there.

Maybe I'm being nitpicky, but I think this is an important distinction. If we're going to be doing math, let's be precise, huh?

(As an aside, I *love* probability as a science, because it's fantastically counter-intuitive and is so important in coming to the correct conclusions about things. I hope to do some posts on probability in the future!)