A country adopted a policy requiring all couples to continue having children until they had a girl, after which they must stop having children. How many children willthe average family have and what will the sex distribution be?
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Answer Posted / Avanish Kumar Pandey
In this scenario, families will continue having children until they have at least one daughter. Let's assume that on average, it takes x births to get a girl after the first boy. The expected number of children per family would then be 1 + x. Since boys and girls are equally likely, the probability of having a boy is 1/2 and the probability of having a girl given a boy is also 1/2 (since we assume that families don't stop until they have a girl). Therefore, the expected number of children per family can be found by solving the equation E(X) = 1 + x * 0.5^x, where E(X) is the expected value of X. This equation is a geometric series with a first term of 1 and a common ratio of 0.5, so we can use the formula for the sum of an infinite geometric series to find E(X). We get E(X) = 2. The sex distribution will be approximately 1 boy and 1 girl.
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