只想生女孩的世界：女孩比例是多少
All-Girl World?
题目详情
一个原始社会中，每对夫妻都想要一个女儿。每个孩子是女孩的概率为 50%，且相互独立。
每对夫妻会一直生孩子直到生出女孩，然后停止。
问：最终人口中女孩所占比例是多少？
In a primitive society, each couple wants to have a baby girl. Every child has a 50% chance of being a girl, and all children’s genders are mutually independent. Each couple keeps having children until they get a girl, then they stop. What fraction of the population will be girls eventually?
解析
仍为 50%。
每次出生的性别仍是独立且女孩概率为 。虽然每个家庭的“停止规则”改变了家庭规模分布，但不会改变总体出生序列中女孩的长期比例（期望与极限比例仍为 1/2）。
Original Explanation
Since each child is equally likely to be a boy or a girl (50% each, independent), the overall ratio of girls to total children stays at 50%. Each couple’s “strategy” does not change this fundamental probability. The fraction of girls is therefore 50%.