“这个盒子下面也是黄金的概率是多少?”这个问题提得有点毛病。既然是“随机的选了上面/下面”,那么所提的问题就应该是:这个盒子的另一面也是黄金的概率是多少? 问题更正以后,并把“随机”理解为服从均匀分布,答案是四分之三。 |
An obvious answer is 2/3 -- did I fall in some trap?
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You are right! The probability is 2/3. To solve this problem, we just need to use the conditional probability. |
Condition on you see a gold box already. What is the sample space now? p=2/3 is not correct. And from the picture of the question, it seems he happen to open a upper box though he randomly choose the box position. |
If what he described in the picture is actual arrangement of the gold in the box (sample space), then Pr(gold | a gold ) =1/2 Pr(gold | an upper box gold) = 1 When you open a box and see a gold, you obviously know: 1) it is a gold in stack, 2) it is upper or lower box. From what the question ask: Bottom Box Gold probability =1 本贴由[NuBHH]最后编辑于:2013-4-27 8:49:40 本贴由[NuBHH]最后编辑于:2013-4-27 8:53:28 |
我的理解: 虽然题中叫"上面"和"下面", 其实这两面是不可分辨的. |
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