# Thread: Simple puzzles to stump people

1. Originally Posted by Zergling
The host is not making a random choice of which door to show you, he (or she) deliberately picks the goat door to show you. If the host had randomly chosen a non-picked door to show you, and that door happened to be a goat, it would be a 1/2 chance. (though in that case he might open up the prize car door instead.)

(For comparison, I didn't figure this out when originally hearing about it either, and it took some convincing also.)
But the point is, I have no way of knowing whether the door I picked originally was the goat or the car one. The host might simply have opened the goat door I didn't choose, or he might have opened one of the goat doors, after I already picked the car door, and I have no way of knowing which he did. I don't see why it's more likely that he did the former.

2. Originally Posted by athenian200
But the point is, I have no way of knowing whether the door I picked originally was the goat or the car one.
No, but you DO know that, at the time, you had a 1 in 3 chance of choosing the car...which is still the case.

3. Originally Posted by oberon67
No, but you DO know that, at the time, you had a 1 in 3 chance of choosing the car...which is still the case.
I just can't help but see the 1/3 as an illusion. Obviously once one is revealed, which will always be an irrelevant one, then only the door you chose and another one remain. There isn't any reason to assume that the door you didn't choose is more likely than the one you did. They both have the potential to be the correct door.

4. Originally Posted by Economica
Once again, if it's any consolation, not a single student in my class of 30 got it right either. And we all knew Bayes' Theorem by heart. :blushing:
Actually, since the witness is always right 80&#37; of the time, doesn't that just mean that there's an 80% chance that it was a Blue cab? The actual quantity/percentage of cabs in the city doesn't matter, does it?

Originally Posted by athenian200
I just can't help but see the 1/3 as an illusion. Obviously once one is revealed, which will always be an irrelevant one, then only the door you chose and another one remain. There isn't any reason to assume that the door you didn't choose is more likely than the one you did. They both have the potential to be the correct door.
Well, just to step outside of it for a moment, note that 2/3 IS the correct answer. Run the simulations, and 2/3 is what the rate of success is, if you switch doors. That's already proven.

So it's more a matter of recalibrating your thinking rather than arguing with the solution.

5. Originally Posted by Jennifer
Actually, since the witness is always right 80% of the time, doesn't that just mean that there's an 80% chance that it was a Blue cab? The actual quantity/percentage of cabs in the city doesn't matter, does it?
That is the wrong answer most people give.

The real answer is 41%. See the Wikipedia link for an explanation.

6. Originally Posted by athenian200
There isn't any reason to assume that the door you didn't choose is more likely than the one you did. They both have the potential to be the correct door.
They both have the potential to be the correct door, that is true. Further, you can quantify that potential. The first door, the one you picked, was randomly selected from three possibilities. The second door represents all the other possibilities.

The elimination of the extra goat door has no bearing on the fact that your odds of choosing correctly were one in three at the time you chose. The value of your choice does not increase by virtue of your subsequently learning where an incorrect choice was.

7. Originally Posted by Jennifer
Well, just to step outside of it for a moment, note that 2/3 IS the correct answer. Run the simulations, and 2/3 is what the rate of success is, if you switch doors. That's already proven.

So it's more a matter of recalibrating your thinking rather than arguing with the solution.
It may be correct mathematically, but I don't think it actually changes the likelihood. I think it's just correct probability due to a technicality in the rules of math rather than any thing that makes sense.

8. Originally Posted by Economica
That is the wrong answer most people give.
Yay! Yay! My first answer was uniquely wrong! Even in my wrongness, I am unique!

But it's still wrong.

9. Originally Posted by athenian200
It may be correct mathematically, but I don't think it actually changes the likelihood. I think it's just correct probability due to a technicality in the rules of math rather than any thing that makes sense.
Um... What???

It DOES change the likelihood.

If you do the test in real life (not theory, REAL life), the answer is 2/3. What on earth are you talking about?

10. Originally Posted by Jennifer
Um... What???

It DOES change the likelihood.

If you do the test in real life (not theory, REAL life), the answer is 2/3. What on earth are you talking about?
Athenian is mistaking his understanding for reality, not an uncommon occurrence.

Remember Russel Crowe in A Beautiful Mind?

"I played perfectly."
"But you lost, nonetheless."
"Then the game was flawed!"

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