Monty Hall Problem
Switching doors wins 2/3 of the time.
Key idea
Switching doors wins 2/3 of the time.
In depth
After you pick one of 3 doors and the host reveals a goat behind another, switching wins with probability 2/3. The host’s action carries information because he never opens the car’s door. Your first pick had 1/3 chance.
Worked example
Out of 3 equally likely car positions, staying wins in 1 case and switching wins in 2.
Real-world uses
- Understanding why switching doors in a game show is the better choice
- Testing intuition with simulation
Common mistake
Claiming the remaining two doors are equally likely.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Monty Hall Problem?
Switching doors wins 2/3 of the time. It is a topic at the advanced level in Probability & Statistics.
Where is Monty Hall Problem used in real life?
Real-world examples: Understanding why switching doors in a game show is the better choice; Testing intuition with simulation.
What should I learn before Monty Hall Problem?
Make sure you are comfortable with Birthday Problem, the previous topic in Probability & Statistics.
What is a common mistake with Monty Hall Problem?
Claiming the remaining two doors are equally likely.
How can I practise Monty Hall Problem?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
Related advanced topics in Probability & Statistics
- Quartiles and IQR – Quartiles split data into four parts; IQR = Q3 − Q1.
- Box Plots – Five-number summary visualised.
- Outliers – Values beyond 1.5 IQR from the quartiles.
- Variance – Average squared deviation from the mean.
- Standard Deviation – Square root of variance; typical spread.
- Sample vs Population Variance – Divide by n−1 for sample variance.