用公平硬币模拟 1/3 与 2/3

simulate an event that has probability $1 / 3$ , and an event that has probability $2 / 3$ .

专题: Probability / 概率
难度: L4
来源: QuantQuestion

个人笔记

题目详情

概率题：用公平硬币模拟 1/3 与 2/3。

英文原题

You have a fair coin and you want to simulate an event that has probability $1 / 3$ , and an event that has probability $2 / 3$ . How do you do it?

解析

抛两次硬币：

HH → 事件 A（概率 $1/3$ ）
HT 或 TH → 事件 B（概率 $2/3$ ）
TT → 丢弃重来

因为在去掉 TT 后，HH/HT/TH 三种结果等概率，因此得到 $1/3$ 与 $2/3$ 。

英文解析

To simulate an event with probability $1 / 3$ using a fair coin, toss the coin twice. If you get $HH$ , let that be your event with probability $1 / 3$ . If you get $HT$ or $TH$ , let that be your event with probability $2 / 3$ . If you get $TT$ , then ignore it, and toss twice again. By removing $TT$ from the sample space, the outcomes are restricted to three equally likely possibilities.