Monty Hall problem

A probability puzzle in which a contestant chooses one of three doors, a host reveals a losing option, and switching to the remaining door raises the chance of winning from one-third to two-thirds.

Conditional probability: The probability of an event given that another event is known to have occurred. The reveal changes the probabilities conditional on the host’s action.
Monty Hall: A Canadian-American game-show host best known for presenting the television show Let's Make a Deal. His name became attached to the puzzle inspired by the show’s door choices.
Bertrand's box paradox: A probability puzzle involving two boxes and the misleading inference that can follow from observing one object. It also exposes how assumptions about selection and observation shape probability answers.
Teaching probability: The instruction and study of how to quantify uncertainty and reason about random events. The puzzle makes conditional probability concrete and exposes faulty intuitions.
Bayes' theorem: A rule for updating probabilities when new evidence becomes available. It formalizes how the revealed door changes the odds for the unopened doors.
Let's Make a Deal: An American television game show in which contestants trade and choose among prizes and concealed options. Its format supplied the puzzle’s familiar doors, prizes, and host.
Three prisoners problem: A probability puzzle about one of three prisoners being pardoned and information revealed by a guard. Its information structure closely parallels the door puzzle.
Probability paradox: A probability problem whose intuitive answer conflicts with a correct analysis under stated assumptions. The puzzle is a classic example of intuition clashing with formal probability.
Sample space: The set of all possible outcomes of a random experiment. Listing prize locations and contestant choices makes the two-thirds strategy visible.
Steve Selvin: An American statistician who posed the three-door puzzle in letters to The American Statistician in 1975. His letters introduced the problem under the name “Monty Hall problem.”

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