Daughters

Borrowing a well-known problem from Leonard Mlodinow’s The Drunkard’s Walk:

Suppose a mother is carrying fraternal twins and wants to know the odds of having two girls, a boy and a girl, and so on. […]  What are the chances she will have at least one girl?

Given the odds of having a boy are equal to the odds of having a girl (50% chance of either occurring), the answer is straightforward. From enumerating all 4 potential outcomes (GG, GB, BG, and BB), we can see that 3 of the 4 outcomes include at least one girl. The chances of having at least one girl are 75%.

Now a related question, which considers the same mother carrying fraternal twins:

What are the chances, given that one of the children is a girl, that both children will be girls?

I’ll post the answer to this one in the comments.

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