Monty Hall with four doors
A game show has four doors: one hides a car, three hide goats. You pick a door. The host, who knows where the car is, opens one of the other three doors to reveal a goat (choosing at random among goat doors if he has a choice). He then offers you the chance to switch to either of the two remaining unopened doors.
- What is your probability of winning if you stay?
- What is it if you switch to one of the two remaining doors at random?
- Suppose instead the host opens two goat doors, leaving one other door. What is the probability of winning by switching then?
Show a hint
Your original door has the car with probability 1/4, and nothing the host does changes that. The remaining 3/4 is shared among the doors he leaves closed.
Your answer
Solving needs a free account
Answers, streaks and solutions unlock when you are signed in. Reading the question and the hint stays free.
Discussion
Sign in to join the discussion · reading is open to everyone
💡 Discussion rules
- No full solutions here. Hints and approaches only.
- Complexity, edge cases and intuition are the point.
- Interview experiences are welcome. Respect your NDAs.
Loading discussion…
Learn the concepts
The theory behind this question.
Related questions
Monty Fall, the host who opens a door by accidentThe hot hand in three coin flipsThe Monty Hall problemThe prosecutor's fallacyTwo bullets side by side, spin or not?
All questions →