The “Stop After a Boy” Population Puzzle

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Easy

ProbabilityExpected Value

A law says that a family may continue having children until it has its first boy, but must stop immediately after a boy is born.

Assume every birth is independently a boy or girl with probability $1/2$ .

Examples of possible families are

$B,\quad GB,\quad GGB,\quad GGGGB,\ldots$

What is the long-run ratio of boys to girls?

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