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I would like to get an answer from someone who knows mathematical definitions, Q: is this claim: "it's possible for something to have probability zero (not approaching, actually zero) and yet be possible." Correct?

elie kalter
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  • Yes, just as in integration theory, aset may have measur $0$ without being empty. – Bernard Nov 27 '19 at 17:55
  • Correct. The probability of a line going through any particular point in $\mathbb{R}^2$ is zero, but obviously it's possible because infinitely many lines go through each point. – Annapox Nov 27 '19 at 17:55
  • Only in the discrete case, $P(A)=0$ means that $A$ is the impossible event. – Peter Nov 27 '19 at 17:55

2 Answers2

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It is possible. $0$ probability doesn't mean impossible. The classic example is the following:

The probability of any given number being chosen from a random number generator over the reals is $0$ (it couldn't be anything else, since there are an infinite number of reals) but the probability of some number being chosen is $1$, so clearly it is possible.

Rushabh Mehta
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$\mathbb{P}(X=0.5)$ where $X$ is a uniform distribution between $]0,1[$

Canardini
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