"Almost Surely" vs "Surely" I'm struggling to understand the concept of "Almost Surely" in probability. I've read the wiki article ( http://en.wikipedia.org/wiki/Almost_surely ) and looked at some old posts on this forum but there's something I still don't get: Given a theoretical coin that lands on either heads or tails: If you flip it infinite times then you could say it will almost surely land on heads at least once. That is, the infinite sequence of T, T, T, T, T etc. is 'almost surely' not going to happen. What I don't understand is if you have a theoretical coin that can be H or T, and it only lands on T, how can it ever be called "a coin that can be H or T". Isn't the definition wrong? Shouldn't it be called "a coin that can only ever be T"? Sorry if that's not a very rigid argument as I don't have the skills to put it in structured mathematical form.