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The probability of each individual outcome is zero.


Cover of Understanding Probability, Third Edition


However, in reality, an individual outcome may happen! Does it mean that a probability of zero does not necessarily mean that an event is impossible? The answer is yes, when dealing with infinite (countable or uncountable) sets. The probability of a single (or finite) outcome out of infinite choices is always zero! This is because, the length of a set containing finite points from an infinite sample space is zero (for example the non-empty set {2} is real numbers has zero length). However, for finite sets, a zero probability is equivalent of impossibility! https://nolaymanleftbehind.wordpress.com/2011/07/13/the-difference-between-impossible-and-zero-probability/