Monty Hall, Generalized
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.
Related problems & prerequisites
Worth solving first
- First Heads Wins 5.0/10
- De Méré's Wager 4.0/10
- Seven Before Eight 3.0/10
Source: Generalisation of the Monty Hall problem, posed by Steve Selvin (1975) and made famous by Marilyn vos Savant (1990). Statement written for AxiomIQ.