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 is the probability of an empty set?

• It depends on the context

• It is always one

• It is always zero

• It can be any value

What is the probability of a sample space?

• It is undefined

• Zero

• One

• Depends on the events

If two events A and B are disjoint, what is the probability of their union?

• Probability of A divided by probability of B

• Probability of A times probability of B

• Probability of A plus probability of B

• Probability of A minus probability of B

Why must the probability of an empty set be zero?

• To make calculations easier

• Because it is a rule of thumb

• To ensure the probability of any event does not exceed one

• Because it is always one

What happens if the probability of an empty set is not zero?

• It would make the probability of sample space zero

• It would have no effect

• It would violate the axiom of probability

• It would be consistent with probability axioms