情趣生活
情趣生活 => 灵机一动 => Topic started by: MrPuzzle on 七月 07, 2004, 08:43:55 am

Yesterday's problem was solved, here's another one. Look for simple explaination.
Neo flips a fair coin 20 times. Agent smith spins a fair coin 21 times. Agent smith wins if he gets more heads than Neo, else Neo wins. Note that Neo wins if there is a tie. What is the probability that Agent smith wins?

0.5 ? Only the 21st flip of Agent Smith matters.

0.5 ? Only the 21st flip of Agent Smith matters.
对。在所有对局中，只看两人前20次投币，如果Neo的正面多于Smith的，则Neo已赢，反之也一样，这两种局面出现次数相同。唯一有悬念的是前20次中两人正面数目相同，则Smith的最后一投决胜负。

Yes, just as Froid explained, the last flip by Smith will set the difference, thus, the probability is 1/2.