Why You Should Switch Doors in the Monty Hall Problem
In the classic game-show puzzle, a player chooses one of three doors, then the informed host opens another door to reveal a goat and offers a switch. Jacobs explains that switching is better because the host's choice is not random; he knows where the prize is, so the switch carries a two-in-three chance rather than an intuitive fifty-fifty chance.
- The original choice has a one-in-three chance of holding the car
- The host deliberately reveals a goat rather than opening a random door
- Switching captures the original two-in-three probability assigned to the other doors
- Even mathematicians objected when Marilyn vos Savant published the answer
“you should switch”
“don't trust your gut i am very wary of my gut”