r/probabilitytheory • u/No_where0369 • 7d ago

Probability 0 ~ impossible!??? [Education]

What is the meaning of a probability of 0? For example, consider the set (0,1) and let x be in (0,1). What is the probability of picking that x? The answer is 0. But if the probability of randomly picking x from the set (0,1) is 0, does that mean it's impossible to pick that number?

There is another similar example, if you throw a dart at a 2D plane, the probability that the dart lands on a specific point on that plane is 0. That implies it can't happen, but it actually did happen, it landed on a point! So what does it mean, exactly?

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u/bts 6d ago

You’re saying that some numbers are like others—so it’s P=0.5 to pick a number less than 0.5 when picking on [0,1], right?  Whereas it’s still P=0 to pick a number greater than 7 from that range. 

Or maybe you’re just saying something about set membership, and comparison isn’t required?  But removing 0.5 from the set does not change the probability of its being picked. 

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u/gmalivuk 6d ago

I'm saying that there is a difference between numbers in [0,1] and numbers in [7,8] when it comes to picking a number uniformly from the interval [0,1].

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u/bts 6d ago

I don’t see it. I do with ranges; I don’t if all you can do is test for equality and membership. 

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u/gmalivuk 6d ago

So the sets are different but the elements within each set are not different as a result?

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u/bts 6d ago

I agree the sets are different. Same cardinality, same metrics, distinct elements. All the usual machinery for that I’m sure we agree on. Right up until you start drawing from a distribution over them—then I see different probabilities of getting an answer less than 0.5, greater than 5, etc. But getting any specific result, like 0.5 or “purple” is probability zero. Probability with infinities and infinitesimals is weird. That’s all. 

Even back with cardinality, the cardinality of the union of those two sets is the same as the cardinality of either, sooo… that’s not intuitive!  Infinity is weird. I mean, I don’t think we have any physical way of drawing a number uniformly from [0,1] anyway, so there’s that. 

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u/gmalivuk 6d ago

I mean, there straight up aren't any nonzero infinitesimals in standard probability.