Probability · Maths EE idea · Accessible
Monty Hall and its variants
A research question to start from
Why should a player switch in the Monty Hall problem, and how does the answer change when the host's behaviour or the number of doors changes?
A starting point, not your question: change the case, the comparison or the limit until it is yours. The research-question builder helps you check it.
Why it works as a maths EE
Conditional probability made precise; the variants force careful modelling of assumptions.
Mathematics you would need
- Conditional probability
- Bayes' theorem
- Tree diagrams
- Modelling assumptions
Much of this goes beyond the DP course. That is expected in a maths EE, but you must understand and explain everything you use.
One possible line of attack
- Solve the classic problem with Bayes' theorem.
- Solve variants (random host, n doors, biased host).
- Discuss why intuition fails and which assumptions matter.
Scope and difficulty
Accessible. Accessible; depth comes from the variants.
Pitfalls
- Only the classic case.
- Unstated assumptions about the host.
Where to start reading
Search a library catalogue or a university's open lecture notes for: Monty Hall Bayes theorem host behaviour variants. Prefer textbooks, lecture notes and journal articles to a single website, and cite everything you use (how to reference a maths EE).