You have to find the hidden prize. First choose a door. One of the others (leading not to the prize!) will then be indicated. You can then choose to either keep your original choice or swap to the other door.
What is the best tactic? Always stick with your original choice? Always swap? Or does it make any difference? What are the probabilities of winning?
What is the best tactic? Always stick with your original choice? Always swap? Or does it make any difference? What are the probabilities of winning?
The BBC web site has a further example and explanation here: Monty Hall
Software/Applets used on this page
From a collection of Java statistics applets from the Project
Interactive, Shodor Educational Foundation site at Durham, North Carolina, USA, used with permission.
Interactive, Shodor Educational Foundation site at Durham, North Carolina, USA, used with permission.
This question appears in the following syllabi:
| Syllabus | Module | Section | Topic | Exam Year |
|---|---|---|---|---|
| AQA A-Level (UK - Pre-2017) | S1 | Probability | Experimental | - |
| AQA AS Maths 2017 | Statistics | Probability | Experimental Probabilities | - |
| AQA AS/A2 Maths 2017 | Statistics | Probability | Experimental Probabilities | - |
| CBSE XII (India) | Probability | Probability | Repeated independent (Bernoulli) trials and binomial distribution | - |
| CBSE XI (India) | Statistics and Probability | Probability | Random experiments, outcomes, sample spaces (set representation) | - |
| CCEA A-Level (NI) | S1 | Probability | Experimental | - |
| CIE A-Level (UK) | S1 | Probability | Experimental | - |
| Edexcel A-Level (UK - Pre-2017) | S1 | Probability | Experimental | - |
| Edexcel AS Maths 2017 | Statistics | Probability | Experimental Probabilities | - |
| Edexcel AS/A2 Maths 2017 | Statistics | Probability | Experimental Probabilities | - |
| I.B. Higher Level | 5 | Probability | Experimental | - |
| I.B. Standard Level | 5 | Probability | Experimental | - |
| Methods (UK) | M15 | Probability | Experimental | - |
| I.B. (MSSL) | 3 | Probability | Experimental | - |
| OCR A-Level (UK - Pre-2017) | S1 | Probability | Experimental | - |
| OCR AS Maths 2017 | Statistics | Probability | Experimental Probabilities | - |
| OCR MEI AS Maths 2017 | Statistics | Probability | Experimental Probabilities | - |
| OCR-MEI A-Level (UK - Pre-2017) | S1 | Probability | Experimental | - |
| Pre-Calculus (US) | E4 | Probability | Experimental | - |
| Pre-U A-Level (UK) | Prob | Probability | Experimental | - |
| Scottish (Highers + Advanced) | HS | Probability | Experimental | - |
| Scottish Highers | S | Probability | Experimental | - |
| Universal (all site questions) | P | Probability | Experimental | - |
| WJEC A-Level (Wales) | S1 | Probability | Experimental | - |