Impossible event

An event that, under the given conditions, cannot possibly occur. If $ ( \Omega , {\mathcal A} , {\mathsf P} ) $ is a probability space, the impossible event is $ \emptyset \in {\mathcal A} $ that does not contain any of the elementary outcomes $ \omega \in \Omega $( the empty set). The impossible event is the complement of the certain event $ \Omega $ in this probability model, and for this reason it is assigned probability zero: $ {\mathsf P} ( \emptyset ) = 0 $.