A few years back, this problem appeared in the column "Ask Marilyn". And Marilyn Vos Savant, the woman who was claimed to have the highest IQ on record, gave the wrong answer. (As usual when it involves statistics problems. ) Furthermore, she refused to recognize her mistake after pointed out by many mathematicians and statisticians. |
我的同时出给我做，我自认为做出来了，但是还没有要结果。 我以前只见过一个类似的题，关于3个门，一个后面有汽车问题。我想大家都知道。。。 |
For the first question, Girl. Probability of 2/3 to be right. For the second, does not matter. Well, I am not good at statistics and my IQ is around 100. Just pour some water here. |
其实，第一个问题是别人出给我做的，第二个问题是我自己想的，所以我下面各处的解答有可能不对。 第一个问题： 他告诉我说，有一个孩子是 男孩，并且让我猜另一个孩子是男孩还是女孩。 问：我应该怎么猜呢？猜男孩的概率大还是猜女孩的概率大？还是一样大？ 情况为4种可能性（b=boy, g=girl, 第一个表示老大，第二个表示老二) bb，bg，gb，gg 有一个孩子是 男孩, 排除了gg 的可能性。所以另一个孩子是女孩子的可能性是 2/3，是男孩子的可能性是 1/3，这个比较好理解。 第二个问题： 如果，他告诉我，老大是男孩，并且让我猜老二是男孩还是女孩。 问：我应该怎么猜呢？猜男孩的概率大还是猜女孩的概率大？还是一样大？情况为4种可能性 bb，bg，gb，gg 第一个孩子是男孩，也就排除了 gg, gb, 而只剩下 bb, bg 所以第二个孩子是男孩，女孩可能性均为50% |
That was correct according to all the mathematicians and statisticians. But Marilyn insisted that it was 50% in both cases. |
50% are boys and 50% are girls. There are millions of boys and millions of girls, one kid is a boy will not change the statistics that much. Therefore, the possibility of the other kid is a girl is still 50%. |
We are not talking about just another child. We are talking about the other child of a two child family, when we already know there is a boy. Among all two child families, 3/4 have at least one boy, and only 1/4 have two boys. |
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