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If the probability of two events are equal, can we conclude that the events are equal? In other words how does one show that the event of getting at most 3 x's is the same as the sum of the events of getting exactly 3 x's and at most 2 x's.

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    @all: Thanks. I knew about showing that one is a subset of the other and vice versa approach. I was hoping that there was another way.2011-09-22

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NO, same probability is not used to define "equality" of events. Instead, just say "equal probability", or be fancy and say "equiprobable".