What is expected value of the sum of the numbers appearing on two fair dice when they are rolled given that the sum of these numbers is at least nine? That is, what is E(X | A) where X is the sum of the numbers appearing on the two dice and A is the event that X ‰¥ 9? The law of total expectation states that if the sample space S is the disjoint union of the events S1, S2, . . . , Sn and X is a random variable, then E(X) =

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Ej=1 E(X|S})P(S}).