Quote:
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Originally Posted by whitepotatoe Quote: |
Originally Posted by R Deckard You're playing "Let's Make a Deal" with Monty Hall. You have a choice of picking Door Number 1, 2, or 3. Behind one of the doors is a fabulous prize, behind the other two doors are gag gifts. The game will proceed as follows: - Monty will first ask you to pick a door.
- After you make your pick, Monty will open one of the other doors. Monty knows what is behind each door, so he will always open a door to one of the gag gifts.
- Monty will then ask you if you want to stay with your initial door selection, or if you want to change it and pick the other remaining closed door.
The Question: What should you do? - Stay with your initial selection
- Switch to the other door
- It doesn't matter, the chances of winning are the same
| B. Switch doors. You increase your chance of being right from 33% to 67%. When you initialy pick, your chances of being right are 33%. When one door is removed, you still have a 33% chance about being right with your initial pick, so that means the other door is the winner 67% of the time.  |
I went and ran through this myself when I found myself saying "that doesn't quite look right" at this answer. Really this answer just confused me since I'm a visual learner. So for the other visual learners out there, look at it this way-
Here are the three doors:
edit: this stupid bb truncates all of my spaces to one space, so the figures will look a little funny.
|---| |---| |---|
| 1 | | 2 | | 3 |
|---| |---| |---|
One with the Prize, two and three with crap:
|---| |---| |---|
| P | | 2 | | 3 |
|---| |---| |---|
We pick one door:
|---| |---| |---|
| P | | X | | 3 |
|---| |---| |---|
Monty nixes a gag door:
|---| |---|
| P | | X |
|---| |---|
What action, if taken, would get us the prize? Switch doors.
Okay, now what would happen if we had started by picking a different door?
|---| |---| |---|
| P | | 2 | | X |
|---| |---| |---|
Monty eliminates door 2:
|---| |---|
| P | | X |
|---| |---|
What action, if taken, gets us the prize? Switch doors.
And the last possibility?
|---| |---| |---|
| X | | 2 | | 3 |
|---| |---| |---|
Monty eliminates a junk door.
|---| |---|
| X | | 2 |
|---| |---|
What action, if taken, gets us the prize? Stay.
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So switching gets you the prize two out of three times. It will be two out of three times for any placement of the prize, so the net probability is that ~67% of the time switching doors get you the new car.
Okay, I know many of you probably understood this anyway, but I figured I'd help some of the straglers with and explanation that made more sense to me as a visual learner.
I'm out!
