Impossible event
From Encyclopedia of Mathematics
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
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