三孩分苹果：公平硬币策略与期望抛掷

Three children but only one apple

专题: Probability / 概率
难度: L4
来源: QuantQuestion

题目详情

You have three children, but only one apple. You want to toss a fair coin to determine which child gets the apple. You want each child to be equally likely to get the apple. What is your strategy? What is the expected number of tosses needed to complete this strategy?

解析

策略：抛两次。HT 给孩子 1，TH 给孩子 2，HH 给孩子 3，TT 重新开始。这样在非 TT 条件下三种结果等概率。

期望抛掷次数 $E$ 满足 $E=\frac34\cdot 2+\frac14(2+E)\Rightarrow E=\frac{8}{3}.$