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Intuitively, I can understand that if an event C occurs with some probability P(C) AND event D occurs with some probability P(D), then drawing a venn diagram of them it wouldn't matter whether the C or D came first.
However, I can't seem to find anything to back this up and thus don't feel comfortable using this 'identity'. Can anyone confirm this for me?

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    Yes. But more fundamentally $C\cup D = D \cup C$ as sets.2011-09-25

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This is always true because $C\cup D = D\cup C$ as sets.