Suppose that k events b1, b2, bk form a partition of the sample space s. for i = 1, k, let p r(bi) denote the prior probability of bi . there is another event a that p r(a) > 0. let p r(bi |a) denote the posterior probability of bi given that the event a has occurred. prove that if p r(b1|a) < p r(b1), then p r(bi |a) > p r(bi) for at least one value of i (i = 2, k). (hint: one or more of these tricks might : p(bi |a)p(a) = p(bi ∧ a), pk i=1 p(bi) = 1, pk i=1 p(bi |a) = 1, p(bi ∧ a) + p(bi ∧ ¬a) = p(bi), pk i=1 p(bi ∧ a) = p(a))