Difficulty: Medium · Puzzle 4 of 6 · Topic: Probability Puzzles
In a 3-door game, one car and two goats. You pick one door, host reveals a goat from a different door, then offers switch. Should you switch?
Initial pick keeps its original probability.
1) Initial chosen door has car with probability 1/3.
2) Therefore car is in one of the other two doors with probability 2/3.
3) Host always opens a goat door among those two, never opening the car door.
4) Host action transfers the full 2/3 mass to the single unopened alternate door.
5) Staying wins with 1/3; switching wins with 2/3.Answer: Switching doubles win probability from 1/3 to 2/3.
Treating final two doors as symmetric 50-50 after reveal.
What changes if host sometimes opens a random door without knowing?