Data Science and Machine Learning (Theory and Projects) A to Z - Probability Model: Probability Axioms Derivations Solut

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.

What conclusion can be drawn about the probability of the empty set based on the probability of the sample space?

Discuss the implications of having a nonzero probability for an empty set.