推 teves:就如同告訴妳兩個孩子中有男孩會刪掉雙女孩的情況使機率 10/25 11:29
→ teves:降成1/3一樣,加上星期二也是使條件機率的分母不同 10/25 11:31
這裡是原文(摘錄)
Stories vs. Statistics
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Consider the two boys problem in probability. Given that a family has two
children and that at least one of them is a boy, what is the probability that
both children are boys? The most common solution notes that there are four
equally likely possibilities — BB, BG, GB, GG, the order of the letters
indicating birth order. Since we’re told that the family has at least one
boy, the GG possibility is eliminated and only one of the remaining three
equally likely possibilities is a family with two boys. Thus the probability
of two boys in the family is 1/3. But how do we come to think that, learn
that, believe that the family has at least one boy? What if instead of being
told that the family has at least one boy, we meet the parents who introduce
us to their son? Then there are only two equally like possibilities — the
other child is a girl or the other child is a boy, and so the probability of
two boys is 1/2.
Many probability problems and statistical surveys are sensitive to their
intensional contexts (the phrasing and ordering of questions, for example).
Consider this relatively new variant of the two boys problem. A couple has
two children and we’re told that at least one of them is a boy born on a
Tuesday. What is the probability the couple has two boys? Believe it or not,
the Tuesday is important, and the answer is 13/27. If we discover the Tuesday
birth in slightly different intensional contexts, however, the answer could
be 1/3 or 1/2.
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為什麼第二段的案例兩個都是男孩的機率是13/27阿....
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