The video tutorial explains why the probability of an empty set is zero. It begins by questioning if an event with no elements can have a nonzero probability and concludes that it cannot. The proof is based on the axioms of probability, particularly the probability of a sample space being one and the union of disjoint events. The tutorial demonstrates that if the empty set had a nonzero probability, it would violate these axioms. The explanation is simplified by expressing the sample space as a union with the empty set, leading to the conclusion that the empty set's probability must be zero.

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