绿苹果与红苹果：篮子空的概率

green apples and red apples

专题: Probability / 概率
难度: L4
来源: QuantQuestion

题目详情

There are $M$ green apples and $N$ red apples in a basket. We take apples out randomly one by one until all the apples left in the basket are red. What is the probability that at the moment we stop the basket is empty?

解析

停止时篮子为空，当且仅当“最后一个留下的苹果是绿苹果”。

把所有 $M+N$ 个苹果随机排列（等价于随机依次取出直到空）。最后一个位置等可能是任意一个苹果，因此为绿的概率是

\boxed{\frac{M}{M+N}}.