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Puzzle Details

I have two children. At least one of them is a boy.

What is the probability that both my children are boys?

My sister also has two children. The older child is a girl.

What is the probability that both her children are girls?

[Ref: ZFCA]

If we list the possible combinations before we're told anything, and listing the eldest child first we have 4 possible outcomes:

Boy-Boy
Boy-Girl
Girl-Boy
Girl-Girl

Since I have two children, and we know that at least one is a boy, there are three equally probable cases: Boy-Boy, Boy-Girl or Girl-Boy. In only one case are both children boys, so the probability that both are boys is 1 in 3.

My sister's situation is different. Knowing that the older child is a girl, there are only two equally probable cases: Girl-Girl or Girl-Boy. Therefore the probability that both children are girls is 1 in 2.

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