# Thread: Simple puzzles to stump people

1. I'm pretty sure that's it.

2. Wait, I think I've got a better explanation of how I figured this out.

When you start, you have 1/3 chance of choosing the car, and 2/3 chance of choosing the goat. So, if you assume that you chose the goat and change your choice, then you will win 2/3 of the time, because that is the percentage of time that it will indeed have been the goat.

The reason is that if you chose the goat, he will be forced to leave the car door closed to reveal the other goat, thus constraining the possibilities. It's only if you chose the car that he could open either of the unchosen doors. And there is only a 1/3 possibility that you chose the car, so that is less likely.

Well, I only have a tertiary Thinking, so it should come as no surprise that this answer took me so ridiculously long to arrive at. Give me a break.

3. Baaaaaaaa.....!

4. Originally Posted by Jennifer
Baaaaaaaa.....!
You don't think that explanation made any sense, then?

5. Originally Posted by athenian200
Wait, I think I've got a better explanation of how I figured this out.

When you start, you have 1/3 chance of choosing the car, and 2/3 chance of choosing the goat. So, if you assume that you chose the goat and change your choice, then you will win 2/3 of the time, because that is the percentage of time that it will indeed have been the goat.
That's right.

6. Originally Posted by athenian200
You don't think that explanation made any sense, then?

(Remember, I'm in "goofy" mode right now.)

Y'all (obie and gatsby and you) are handling everything nicely, so I will just sit here and provide [not so] comic relief.

7. Originally Posted by Jennifer
I always loved the Monty Hall problem. I remember when Marilyn vos Savant covered it in her column and had to deal for weeks with people writing in and arguing with her about it.

There's also the Shared Birthday problem (i.e., you only need about 35-40 people in one room in order to ensure that at least two of them will have the same birthday... and NOT 365 people as most would think).
Actually the birthday paradox is about how many randomly selected people is needed to make it probable for some of them to share a birthday, if you dont mind being corrected.. "probable" meaning more probable than not, or >.5

8. A complete aside... I struggled with the door problem for a little while until I did the tree (a while back)... But I was able to solve the cab problem without a second thought... The card problem, however, I could barely grasp. I still have to force myself to think about it when faced with the problem.

I wonder what the difference between each of those was, for me... hrmmm.

9. Originally Posted by ptgatsby
A complete aside... I struggled with the door problem for a little while until I did the tree (a while back)... But I was able to solve the cab problem without a second thought... The card problem, however, I could barely grasp. I still have to force myself to think about it when faced with the problem. I wonder what the difference between each of those was, for me... hrmmm.
Gaaa... The cab problem, I would NEVER have gotten when I read the answer.
But I would have reasoned out the card problem.

Perhaps it's simply the level of abstraction involved? There seemed much more to quantify in the cab problem. (This would also explain while I did better in abstract math, while I flunked high-level Statistics.)

Originally Posted by Santtu
Actually the birthday paradox is about how many randomly selected people is needed to make it probable for some of them to share a birthday, if you dont mind being corrected..
Nope, no problem -- thank you!

10. Originally Posted by Jennifer
Gaaa... The cab problem, I would NEVER have gotten when I read the answer.
But I would have reasoned out the card problem.

Perhaps it's simply the level of abstraction involved? There seemed much more to quantify in the cab problem.
That might be it... But in my head, I just quickly went "Chance of seeing + chance of seeing = chance", if you will. It was abstract and not accurate, but the foundation of what was happening was instant.

But I could barely grasp what the card problem was even asking. I read it so many times and still couldn't see where it was going.

The door problem confused me until I saw on paper, if you will.

Geeze, sure sounds like a S:N thing, actually. 1) application, 2) abstraction, 3) evidence.

S = Strong 1, weak 2, moderate 3.
N = Weak 1, strong/moderate 2, moderate/strong 3 (?)

Or maybe it's more granular than that, based on solutions we have had to solve before...

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