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

Title: Coin flip
Post 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?
Title: Coin flip
Post by: packman on 七月 07, 2004, 08:58:18 am
0.5 ? Only the 21st flip of Agent Smith matters.
Title: Coin flip
Post by: froid on 七月 07, 2004, 10:01:58 am
Quote from: packman
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。
Title: Coin flip
Post by: MrPuzzle on 七月 08, 2004, 08:44:10 am
Yes, just as Froid explained, the last flip by Smith will set the difference, thus, the probability is 1/2.