Switch or stay
Open the doors, inspect the host’s rule and test when switching really helps.
A host who knows or a host who guesses
1 question · No time limit
Example
Example
Given this exact reveal and the host’s rule, which action has the greater chance of winning the prize?
One prize was placed uniformly behind 3 doors. You chose door 3. The host does not know where the prize is. The host picks one other door uniformly to keep closed and opens all the rest, even if this could show the prize. This time, no opened door showed the prize. Opened door numbers: 2. Door 1 is the only other closed door.
1. Predict
Make a prediction first. It is not scored.
2. Test your idea
Run the experiment to compare the outcomes.
These are random trials, not exact probabilities.
Try the controls, then check your solution.
Why?
The same random reveal set is equally likely whether the prize is behind your chosen door or the alternative. The opened doors were empty, which rules them out and leaves equal conditional weights.
After this reveal: staying wins with probability 1/2; switching wins with probability 1/2.
Revisit your prediction
Keep exploring the experiment.
3. Change the rules
A linked challenge. This answer is not scored.
Continue your unfinished round
Your answers are saved in this tab. Continue from where you left off.
Continuing uses no additional practice start.
Discard the unfinished round?
Your answers from this round will be discarded. You can choose your settings before starting a new round.
Starting the new round uses one practice start.
- Answered
- 0 / 1
- Active time
- 0:00
Round complete.
Optional and off by default. Share starts, completions, replays and error categories. For visits from ChatGPT, starts and completions can also include the first QuickenBrain page and broad country. No answers, drawings or names.
How this data is usedHelp
Try the controls, then check your solution.
Your first checked solution is recorded. You can keep experimenting afterwards.
About this practice
Learn a method
Follow the host ruleOpen the doors, inspect the host’s rule and test when switching really helps.
For a broader mix of practices, explore the probability practice test. Membership is required to start a test.
Report a problem
Optional and off by default. Share starts, completions, replays and error categories. For visits from ChatGPT, starts and completions can also include the first QuickenBrain page and broad country. No answers, drawings or names.
How this data is used