Brain Puzzle Time
>> 07 August 2009
Several months ago, I posted the first ever Brain Puzzle on this e-blog.
The Smith's have two children; at least one of the children is a girl. What is the probability that both children are girls?
Share your answers in the comments section!
3 comments:
The problem I'm having here is that there's an ambiguity in the way your sentences are structured. If you're saying, essentially, "assuming that at least one of the children is a girl, what is the probability that both children are girls?" then the answer is 50%, because if we can assume that one of them is a girl, then the other one either is or isn't a girl. With that in mind, the probability that there are two girls is 1/2, or 50%.
If, however, the statement that at least one of them is a girl is NOT an assumption used by the probability, then the answer is 33%. We can assume that the following are possibilities:
- One is a boy and the other is a boy.
- One is a girl and the other is a boy.
- One is a boy and the other is a girl.
- One is a girl and the other is a girl.
Note that the puzzle doesn't specify which one of the two is a girl; as a result, the boy/girl split has to be accounted for twice (since each of the two cases has a boy and a girl in it).
Of the four options listed above, there are three that include at least one girl. Only one of those three contains two girls. Therefore the probability is 1/3, or 33%.
Christian and I say 50%.
25%
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