30 minutes ago, dimreepr said:

I was thinking in terms of the universe and the space it takes up, I think, as in an infinite boundary does not = infite monkey's.

My apologies for not understanding the math to explain myself more correctly or fully understand your point, but thanks for your patience.

I think you're getting confused here. Space itself is not of a statistical nature. Things going on in space are. Space is just a backcloth of everything else.

You cannot set up a proper statistical question that involves only space with nothing in it. Wally can be here or Wally can be there. But there's nothing to be done with here and there without some kind of Wally.

16 hours ago, studiot said:

ou need to be careful in your specification of 'an event'

That is correct.
So if the question specifies the event
"what is the probability of any one horse winning the race" then

18 hours ago, MigL said:

In effect, the probability of any one of the horses winning the race is 1/6 .

Of course you can ask "what is the probability of any event happening", which would also include a dead heat, all disqualified, and many more; but that is not what was asked.
Just as in @joigus' original post, the paradox is in the wording of the question; not with the probabilities themselves.

On 5/9/2026 at 2:09 PM, joigus said:

I think you're getting confused here

Probably.

On 5/9/2026 at 2:09 PM, joigus said:

You cannot set up a proper statistical question that involves only space with nothing in it. Wally can be here or Wally can be there. But there's nothing to be done with here and there without some kind of Wally.

Indeed, but isn't that wally some kind of reality?

56 minutes ago, dimreepr said:

Indeed, but isn't that wally some kind of reality?

Depends on how you define a reality. It would be essentially different from 'red, blue, and green' reality if we have to make room for quantum mechanics of spin. But that would take us off on a tangent.

Edited Sunday at 03:53 PM2 days by joigus
minor addition

On 5/9/2026 at 3:35 PM, MigL said:

That is correct.
So if the question specifies the event
"what is the probability of any one horse winning the race" then

Of course you can ask "what is the probability of any event happening", which would also include a dead heat, all disqualified, and many more; but that is not what was asked.
Just as in @joigus' original post, the paradox is in the wording of the question; not with the probabilities themselves.

I disagreed with you 1/6 then and I disagree with it now.

A horse may come in first, second, third, fourth, fifth, sixth or be unplaced.

I make that 7 possible outcomes for any given horse, making the race sample space 6 x 7 = 42 outcomes.

An event is not the same as an outcome, since it is a subset of the set that forms the sample space.

The problem arises that the 7 possibilities are not equally likely, even in theory, so you cannot simply divide by 42.

I don't mind your disagreement, but your reasoning is flawed.

13 hours ago, studiot said:

I make that 7 possible outcomes for any given horse, making the race sample space 6 x 7 = 42 outcomes.

Disregarding the 'unplaced' outcome for now, if one horse places 1st, there are only 5 horses that can place 2nd, and 4 that can place 3rd, and so on, leaving only one horse to place last.
Your sample space, for all possible 'placed' outcomes, would be 6!.

But there are only 6 possible outcomes for winning the race; who/what else could win, other than one of the 6 horses ?

5 hours ago, MigL said:

I don't mind your disagreement, but your reasoning is flawed.

Disregarding the 'unplaced' outcome for now, if one horse places 1st, there are only 5 horses that can place 2nd, and 4 that can place 3rd, and so on, leaving only one horse to place last.
Your sample space, for all possible 'placed' outcomes, would be 6!.

But there are only 6 possible outcomes for winning the race; who/what else could win, other than one of the 6 horses ?

Yes you are correct the factorial is more appropriate than the product.

Thank you for noticing that.

However your basis is still incorrect and if you look back you will notice that each time you have estimated probabilities you have changed the basis .

In particular ignoring the unplaced scenario (I have lumped various possibilities such as rider falls off, horse does not actually start from the starting point, horse falls etc into a single category but all of these have actually happened)

I hope you will agree that 1/6 > 1/7, so even if the unplaced scenario did not occur, it is always a possibility for each and every horse which needs must have an associated probability.

So 1/6 is too large as adding in these probabilities would take 6 times 1/6 plus whatever to greater than 1 .

This is quite different from the situation with the die since no comparable outcome is possible.

That is why statisticians like using coins or dice as examples.