the probability that some elementary event in the entire sample space will occur is 1
I believe that a part of the post's point is that the entire sample space is hard to find in most real-life cases. From the post:
However, in the real world, when you roll a die, it doesn't literally have infinite certainty of coming up some number between 1 and 6. The die might land on its edge; or get struck by a meteor; or the Dark Lords of the Matrix might reach in and write "37" on one side.
EDIT: Another example, this time from the Martin Gardner's excellent book, Mathematical Games :
The hotel's cocktail lounge before the dinner hour was noisy with prestidigitators. At the bar I ran into my old friend "Bet a Nickel" Nick, a blackjack dealer from Las Vegas who likes to keep up with the latest in card magic. The nickname derives from his habit of perpetually making five-cent bets on peculiar propositions. Everybody knows his bets have "catches" to them, but who cares about a nickel? It was worth five cents just to find out what he was up to. "Any new bar bets, Nick?" I asked. "Particularly bets with probability angles?"
Nick slapped a dime on the counter beside his glass of beer. "If I hold this dime several inches above the top of the bar and drop it, chances are one-half it falls heads, one-half it falls tails, right ?"
"Right," I said.
"Betcha a nickel," said Nick, "it lands on its edge and stays there."
"O.K.," I said.
Nick dunked the dime in his beer, placed it against the side of his glass and let it go. It slid down the straight side, landed on its edge and stayed on its edge, held to the glass by the beer's adhesion. I handed Nick a nickel. Everybody laughed.
Nick tore a paper match out of a folder, marked one side of the match with a pencil. "If I drop this match, chances are fifty-fifty it falls marked side up, right?" I nodded. "Betcha a nickel," he went on, "that it falls on its edge, like the dime."
"It's a bet," I said.
Nick dropped the match. But before doing so, he bent it into the shape of a V. Of course it fell on its edge and I lost another nickel.
Today's post, 0 And 1 Are Not Probabilities was originally published on 10 January 2008. A summary (taken from the LW wiki):
Discuss the post here (rather than in the comments to the original post).
This post is part of the Rerunning the Sequences series, where we'll be going through Eliezer Yudkowsky's old posts in order so that people who are interested can (re-)read and discuss them. The previous post was Infinite Certainty, and you can use the sequence_reruns tag or rss feed to follow the rest of the series.
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