The “paradox” may become apparent if you think the answer to all the questions below is the same (2/3). And if it’s not the same, why not?

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You meet three people:

Alice has two children. You're told that at least one of them is a girl.

Bob has two children. You're told that at least one of them is a boy.

Csilla has two children. You're told that at least one of them is a lány. That clearly meant boy or girl because of the context, but you don’t know enough Hungarian to know what it is.

For each of them, what's the probability that they have a girl and a boy?

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You meet all the parents with two children in your neighborhood. Say there are 60 such families.

For 30 of them you’re told that at least one of them is a boy. What's the probability that they have a girl and a boy?

For the other 30 you’re told that at least one of them is a girl. What's the probability that they have a girl and a boy?