Alien Babies Puzzle

We know that every household will have exactly one girl in the end.

What about boys? Sometimes the first child is already a girl (no boys). Other times a family might have one boy before their girl, or two boys, or three, and so on. The odds of those longer streaks drop by half each time: 1 boy happens 1/4 of the time, 2 boys 1/8 of the time, 3 boys 1/16, and so forth. When you add up all those shrinking chances, the average works out to exactly one boy per family.

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