Question: Suppose that k events B1, . . . , Bk form a partition of the sample space S. For i = 1, . . .

Suppose that k events B1, . . . , Bk form a partition of the sample space S. For i = 1, . . . , k, let Pr(Bi) denote the prior probability of Bi . Also, for each event A such that Pr(A) > 0, let Pr(Bi|A) denote the posterior probability of Bi given that the event A has occurred. Prove that if Pr(B1|A) < Pr(B1), then Pr(Bi |A) > Pr(Bi) for at least one value of i (i = 2, . . . , k).

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