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.
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:
EDIT: Another example, this time from the Martin Gardner’s excellent book, Mathematical Games :