Understanding the probability of a point, it's zero but point is observable.

Asked Apr 01 '19 at 16:53

Active Apr 01 '19 at 16:53

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Okay so this might be a basic question/stupid question, but I cannot find an answer for it.

So let's say we have a continuous random variable that returns a value in 0, 1. I know that the probability to observe any single given point in this interval is zero (one point over infinite). How come I can observe this point that has no probability to be observed ?

asked Apr 01 '19 at 16:53

Nuncy588

Also see https://math.stackexchange.com/questions/41107/zero-probability-and-impossibility – Nate Eldredge Apr 01 '19 at 16:55
1

The short answer is "that's just the way probability works". As Von Neumann once said, "in mathematics, you don't understand things, you just get used to them". – Nate Eldredge Apr 01 '19 at 16:56
You seem to be conflating "probability $0$" with "impossible". – Andreas Blass Apr 01 '19 at 18:08

Understanding the probability of a point, it's zero but point is observable.

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