Solution
Monty Hall, Generalized
Show the problem again
You are on a game show with 4 doors. One hides a prize, three hide nothing. You pick a door. The host, who knows where the prize is, opens 2 of the remaining 3 doors (always revealing no prize). You may switch to the one remaining unopened door. What is the probability of winning if you switch? Express as a fraction.
Worked solution
The answer is 3/4. Your initial pick has a 1/4 chance of being correct. The remaining 3/4 probability is concentrated on the other doors. After the host opens 2 empty doors, all 3/4 of that probability collapses onto the single remaining door. Switching wins with probability 3/4.
Source: Generalisation of the Monty Hall problem, posed by Steve Selvin (1975) and made famous by Marilyn vos Savant (1990). Statement written for AxiomIQ.