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In a family with two children, what are the chances, if one of the children is a girl, that both children are girls?

I was able to understand the difference between selecting a child and a family, for the conditional probability question above. However, there is a follow-up paragraph about this question that I do not understand. In my textbook Fundamentals of Probability with Stochastic Processes, it says

picture mentioned

Is the sentence "In fact, the probability that a family with two girls is selected equals twice the probability that a family with one girl is selected." referring to when a child is selected, rather than when a family itself is selected? The entire paragraph was very confusing -- I did not understand the context that the author is explaining. How can P(girl, girl) = 1/2? In what context is the last sentence from?

belle
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1 Answers1

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Suppose there are four families with two children each. One family has a (boy,boy), one a (boy,girl), a (girl,boy) and a (girl,girl). Out of these 8 children, you pick one, which turns out to be a girl. There are four ways to pick a girl, and in half the cases that girl is from the (girl,girl) family.

LinAlg
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