  This paper considers the notion of possible events which are insignificant in
probabilistic analysis (i.e. events that have zero probability). The paper
discusses the method of modal logic based on "possible worlds" and discusses a
mathematical framework for the concepts of possibility, impossibility and
certainty that are sometimes (incorrectly) thought to be defined with respect
to probability. The relationship between possibility and probability is
explored for general probability spaces and for refinements of these spaces
conditional on other events, with particular focus on the properties of events
having zero probability. We derive conditions under which possibility and
significance diverge and conditions under which they can be reconciled as
equivalent ideas within certain contexts. We also apply this analysis to
discuss issues in possibility and probability in the multinomial model.
