HMMT 二月 2000 · GEN 赛 · 第 6 题

HMMT February 2000 — GEN Round — Problem 6

Three ards, only one of whi h is an a e, are pla ed fa e do wn on a table. Y ou sele t one, but do not lo ok at it. The dealer turns o v er one of the other ards, whi h is not the a e (if neither are, he pi ks one of them randomly to turn o v er). Y ou get a han e to hange y our hoi e and pi k either of the remaining t w o fa e-do wn ards. If y ou sele ted the ards so as to maximize the han e of nding the a e on the se ond try , what is the probabilit y that y ou sele ted it on the (a) rst try? (b) se ond try? p

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