Practice question · Multiple choice
The Monty Hall problem: three doors, you pick one, the host opens a different door revealing a goat and offers a switch. Switching wins two thirds of the time. Why does the host's action change the odds?
Hints
- Ask whether the host could have opened the prize door. What does his constraint tell you?
- Play it with a hundred doors: you pick one, the host opens ninety-eight goats. Switch?
Show the answer
A. Because the host knows where the prize is, so his choice informs
Why
Your door held 1/3 and still does; the other two held 2/3 between them, and the host, who cannot open the prize, has funnelled all of it onto one door. The hundred-door version makes it obvious, and the puzzle's fame comes from how firmly the wrong answer resists correction.
Practise Introduction to Probability
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