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https://en.m.wikipedia.org/wiki/Probability_space
That's pretty good. But what about a horse race? The sample space I care about is the number of horses in the race, not the names of the horses, or their race number etc.
The chance of Shergar winning a 7 horse race is 1 in 7. The sample space is 7?
Try it out "Good day. Tell me what is your current probability measure for the event "Shergar wins" from the sample space "The 3:20 at Doncaster"."
I'm sure any bookie worth his salt will give you a knowing nod and take your money with trepidation.
I had to study statistics as part of my accuntancy qualification. In 35+ years nobody has come to me with a bag of blue and red balls and asked what the probability was that the next ball he/she would pick would be blue. If you want a blue ball, open the bloody bag and pick one.