HMMT 二月 2000 · GEN 赛 · 第 6 题

英文原题

6. Three ards, only one of which is an a e, are pla ed fa e do wn on a table. Y ou selectone, but do not lo ok at it. The dealer turns o v er one of the other ards, which is notthe a e (if neither are, he pi ks one of them randomly to turn o v er). Y ou get a han eto hange y our hoi e and pi k either of the remaining t w o fa e-do wn ards. If y ousele 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