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Impossible event

From Encyclopedia of Mathematics
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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 $.

How to Cite This Entry:
Impossible event. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Impossible_event&oldid=47322
This article was adapted from an original article by A.V. Prokhorov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article