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藏在门后的轿车

  • 2026-05-07 22:50:13
藏在门后的轿车
       “蒙特·霍尔问题”亦称“三门问题”，源于一档电视节目中的有奖游戏。
      主持人蒙特·霍尔指点着三扇关着的门告诉参赛者，这是一个考验运气的大奖游戏。其中一扇门的后面有一辆高级轿车，另两扇门后面则各有一只山羊。你要在三扇门中选择一扇，主持人会当众打开，若选中轿车，就可以开车离开，若选中的是山羊，那就准备去放羊吧！于是，刺激的游戏在笑声和期待中开场了。
                           图片来自网络
      就在又一个参赛者选定一扇门时，经验丰富的主持人并没有立刻开启，为了更大程度地营造紧张气氛，灵机一动的他随手打开剩下两扇门中的一扇，一只山羊舔着舌头慢慢地走了出来。这时，蒙特·霍尔转头问参赛者：“现在给你一个机会，我允许你改变原来的选择。你要不要转换为另一扇仍然关着的门呢？”此言一出，参赛者和观众都纠结了。
      大家面对的问题是：如此转换能否增加获得汽车的机会？这也自然引起了数学人士的关注和讨论。他们得出的结论是应该转换。解释的理由并不复杂，我们可以列出游戏可能出现的三种情形：
  1. 参赛者挑中山羊1，主持人挑中山羊2，开启此门――如果转换，参赛者将赢得汽车。
  2. 参赛者挑中山羊2，主持人挑中山羊1，开启此门――如果转换，参赛者将赢得汽车。
  3. 参赛者挑中了汽车，主持人挑中两头山羊中的一头，开启此门――如果不转换，参赛者将赢得汽车。
      也就是说，如果参赛者坚持原先的选择，那么赢得汽车的机会为；如果同意转换，那么赢得汽车的机会将增加到。显然，为了增加赢得汽车的可能，无论参赛者开始的选择如何，在被主持人问到是否转换时，都应该同意转换。
                               图片来自网络
      值得注意的是，转换的前提是游戏者的最初选择在先，否则，主持人先于游戏者随便打开一扇门，问题就发生了改变。一是可能直接打开汽车门，游戏结束；二是可能打开山羊门，这时游戏者再进行选择，得到汽车的机会就是。
      看得出，虽然该问题的答案在逻辑上并不自相矛盾，但十分违反直觉，所以此题曾引起热议。本来这只是一个娱乐节目，可其中有关随机性的数学话题竟然成为热点，并被公众津津乐道，这恐怕是蒙特·霍尔当初也始料未及的吧。
本文来自网友投稿或网络内容，如有侵犯您的权益请联系我们删除，联系邮箱：wyl860211@qq.com 。

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  1. CONNECT:[ UseTime:0.000439s ] mysql:host=127.0.0.1;port=3306;dbname=e_mffb;charset=utf8mb4
  2. SHOW FULL COLUMNS FROM `fenlei` [ RunTime:0.000687s ]
  3. SELECT * FROM `fenlei` WHERE `fid` = 0 [ RunTime:0.000315s ]
  4. SELECT * FROM `fenlei` WHERE `fid` = 63 [ RunTime:0.003180s ]
  5. SHOW FULL COLUMNS FROM `set` [ RunTime:0.000621s ]
  6. SELECT * FROM `set` [ RunTime:0.000797s ]
  7. SHOW FULL COLUMNS FROM `article` [ RunTime:0.000567s ]
  8. SELECT * FROM `article` WHERE `id` = 485800 LIMIT 1 [ RunTime:0.004542s ]
  9. UPDATE `article` SET `lasttime` = 1778375142 WHERE `id` = 485800 [ RunTime:0.002717s ]
  10. SELECT * FROM `fenlei` WHERE `id` = 64 LIMIT 1 [ RunTime:0.001135s ]
  11. SELECT * FROM `article` WHERE `id` < 485800 ORDER BY `id` DESC LIMIT 1 [ RunTime:0.019607s ]
  12. SELECT * FROM `article` WHERE `id` > 485800 ORDER BY `id` ASC LIMIT 1 [ RunTime:0.007352s ]
  13. SELECT * FROM `article` WHERE `id` < 485800 ORDER BY `id` DESC LIMIT 10 [ RunTime:0.010242s ]
  14. SELECT * FROM `article` WHERE `id` < 485800 ORDER BY `id` DESC LIMIT 10,10 [ RunTime:0.016570s ]
  15. SELECT * FROM `article` WHERE `id` < 485800 ORDER BY `id` DESC LIMIT 20,10 [ RunTime:0.067548s ]
0.229255s