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From Probability and Random Processes by Geoffrey Grimmett and David Stirzaker-

An event $A$ is called null if $\Bbb{P}(A)=0$. Null events should not be confused with the impossible event $\emptyset$. Null events are happening all around us, even though they have zero probability; after all, what is the chance that a dart strikes any given point of the target at which it is thrown? That is, the impossible event is null, but null events need not be impossible.

Doesn't a probability of $0$ mean that the event cannot happen just like a probability of $1$ means that the event has to happen?

Robin
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    For something continuous, like the uniform distribution on $[0,1]$, any particular value has probability $0$, but of course it is possible to get a particular value. – lulu Mar 08 '23 at 21:15
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    Note that the term "null event" hasn't got a universally accepted meaning. Some writers, as here, say it means "probability $0$". Others say it means "an event that can not occur". Context should determine which meaning is intended. – lulu Mar 08 '23 at 21:17
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    "Doesn't a probability of 0 mean that the event cannot happen just like a probability of 1 means that the event has to happen?" No, neither of those things is true. :-D – Brian Tung Mar 08 '23 at 22:13

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