蒙提霍尔问题：该不该换门
Monty Hall Problem
题目详情
你在 3 扇门中选 1 扇：1 扇后是汽车，2 扇后是山羊。
主持人会打开另外两扇门中的一扇，并且他知道那扇门后一定是山羊。
此时你可以选择坚持原门或换到剩下那扇未打开的门。
问：你应该换门吗？换门后赢车的概率是多少？
You choose 1 of 3 doors: one hides a car, two hide goats. The host, Monty Hall, then opens one of the other doors that he knows has a goat. You may then stay or switch to the remaining closed door. Should you switch, and what is your probability of winning the car if you do?
解析
应该换门。
- 坚持原门：赢车概率 。
- 换门：赢车概率 。
原因：你最初选对车的概率只有 ；若最初选错（概率 ），主持人会帮你排除另一个错门，换门就必然选到车。
Original Explanation
- Staying with your first door: probability
- Switching: probability