But I will do textmining to the words of the examiner ...to test his behaviorial trend...
And then I can know why he give me a chance to change the boxes...
The result will be added weight on the 50% probability.Although it maybe just 0.0001% difference,I will win...
But you know,lots of Chinese management have no idea abt this common sense...作者: shiyiming 时间: 2008-4-26 21:50 标题: 这是标准答案，不过我是没有看明白，汗！ 答案是应该换.首先你随机拿出一个盒子,那么这个盒子有球的概率是1/3,而另外两个盒子看做一个整体,有球的概率是2/3.现在在明确一个盒子没球的情况下,显然是另外两个盒子中的另一只概率更大.主要是因为打开了其中一个盒子,对两个盒子构成的整体而言,提供了新的信息量.
建立数学模型如下:设变量xi,若第i个盒子有球,则xi=1,若无,xi=0,显然因该取数学期望最大的xi所对应的i值所代表的盒子号.
对于第一个盒子,E(x1)=(1/3)*1+(2/3)*0=1/3,对打开的那只盒子,显然E(x2)=0;现在来考虑第三个盒子,设两个盒子共同有球为事件A,则P(A)=P(A2orA3),因为在”球在这两个盒子中的一只中”这个前提下,A3和A2是互斥事件,所以P(A)=2/3=P (A2orA3)=P(A2)+P(A3)-P(A2andA3)=P(A2)+P(A3),因为P(A2)=0(因为盒子已经打开),所以,P(A3) =2/3,所以,E(x3)=(2/3)*1+(1/3)*0=2/3,综上,应该交换.
以上结论可能有些同学会迷惑，每个盒子有球的概率不是相等的吗，怎么会概率差出一倍出来？其实，完全可以用做实验来解决，你每次任取一个盒子，然后打开剩下的盒子中没有球的一个。注意，问题就出在这里，你怎么能保证每次首先打开的那个盒子是没有球的？显然，当”不幸”你先打开的那个盒子是有球的盒子时，你只能合上重新打开另外一个盒子，而且，在实验中，你有1/3的机会会做这样的事情，所以一个打开的空盒子实际上已经为我们提供了另个盒子的信息量，你没拿在手上的那只盒子有球的概率就增大了。因为有三分之一的情况实际上是，你已经看到了有球，然后关闭的盒子，这三分之一次情况里，它是100%有球的。作者: shiyiming 时间: 2008-4-27 15:31 标题: Re: 趣味问答：盒子、球与概率 hehe~
u guys did too much academic research.
But if u r the examiner ,how do u make sure [b:e0gpq67b]这个盒子是空的[/b:e0gpq67b]? <!-- s:) --><img src="{SMILIES_PATH}/icon_smile.gif" alt=":)" title="Smile" /><!-- s:) -->
And in real world,can u find a noodle who tests u and low the risk of ur choice?
u know if the box opened with a ball,the test can not make any sense,also can not continue...
But the examiner always opens an empty box....
So it's an ancient trick.Some Gypsies earned a lot by this trick as far as I know.
When u play this game,it's not free,u must pay 1 every turn,but can get 100 if u win. <!-- s:D --><img src="{SMILIES_PATH}/icon_biggrin.gif" alt=":D" title="Very Happy" /><!-- s:D -->
The key is [b:e0gpq67b]打开其中一个，这个盒子是空的[/b:e0gpq67b],it's a random event or a sure event <!-- s:) --><img src="{SMILIES_PATH}/icon_smile.gif" alt=":)" title="Smile" /><!-- s:) -->
For this test online,it's a sure event ,'cause everyone here just can encounter the only condition--the box opened is empty.
So it comes to another question,If u know the P=50%,and u must pay for play the game,will u attend? <!-- s:lol: --><img src="{SMILIES_PATH}/icon_lol.gif" alt=":lol:" title="Laughing" /><!-- s:lol: -->