This led me to the concept of events that happen almost surely, which is to say they occur with probability one; alternatively, events that happen almost never have zero probability of occurring. There's nothing too crazy here; an event that happens almost surely simply has an infinitesimally small chance of not happening. So for mathematical purposes it only makes sense to assign the probability as one. To quote the Wikipedia article, "the difference between an event being

*almost sure*and

*sure*is the the same as the subtle difference between something happening

*with probability one*and happening

*always*."

Examples of events that happen almost surely are: flipping a coin an infinite number of times and getting tails at least once, picking a random real number between 0 and 1 and getting an irrational number. Examples of events that happen that happen almost never are: a random variable drawn from a continuous probability distribution taking a particular value, picking a random real number between 0 and 1 and getting 0.5. Moreover, the complement of an almost sure event happens almost never and vice versa. So, to sum things up, an event that happens with probability zero might not

*never*happen, just

*almost never*happen.

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