三孩分苹果

抛两次硬币，令

• HT → 给孩子 1
• TH → 给孩子 2
• HH → 给孩子 3
• TT → 重新开始

因为在“非 TT”的条件下，HT/TH/HH 等概率，所以每个孩子得到苹果概率均为 $1/3$。

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英文解析

There are many different possible answers; I give only two. Toss the coin

twice. If you get $HT$ , give the apple to the first child. If you get $TH$ , give the apple to the second child. If you get $HH$ , give the apple to the third child. If you get $TT$ , then start again. This effectively takes $TT$ out of the sample space.

A second solution is to toss the coin three times and assign the outcomes to the three children. Let $T$ win. If one child beats the other two (i.e., the outcome is some permutation of $\{T, H, H\}$ ), then give the apple to the child who was allocated the $T$ . Otherwise, toss three more times. This is isomorphic to a tournament where each child competes against each other child until one child beats both others.