The Monty Hall problem is famously unintuitive. This post starts with an extreme version where the solution is blindingly obvious. We then go through a series of small changes. It will be clear that these don’t affect the solution.
The way I understood the intuition behind the Monty hall problem is so:
1. You've got a million doors
2. Only one door has a prize
3. Imagine what the probability is that you pick one at random (one in a million)
4. Pick one at random
5. Randomly open 99998 doors that you did not pick and do not contain prizes.
6. 2 doors are remaining, one of which you picked.
7. Has the probability that you picked the correct door changed?
8. If yes, why yes? and if no why no? And what is the new probability?
The Monty Hall problem is famously unintuitive. This post starts with an extreme version where the solution is blindingly obvious. We then go through a series of small changes. It will be clear that these don’t affect the solution.