Suppose you're a contestant on a game show. You're presented with three transparent closed doors. Behind one of the doors is a car, and behind the other two doors are goats. You want to win the car.
The game proceeds as follows: You choose one of the doors, but you don't open it yet, ((but since it's transparent, you can see the car is behind it)). The host, Monty Hall, who knows what's behind each door, opens one of the other two doors, revealing a goat. Now, you have a choice to make. Do you stick with your original choice or switch to the other unopened door?
GPT4 solves it correctly while GPT3.5 falls for it everytime.
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Edit: GPT4 fails If I remove the sentence between (()).
GPT4 also passes "What weighs more, a pound of feathers or a Great British Pound?".
GPT3 gets confused, says they're the same and then that they're different:
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Both a pound of feathers and a Great British Pound weigh the same amount, which is one pound. However, they are different in terms of their units of measurement and physical properties.
A pound of feathers is a unit of weight commonly used in the imperial system of measurement, while a Great British Pound is a unit of currency used in the United Kingdom. One pound (lb) in weight is equivalent to 0.453592 kilograms (kg).
Therefore, a pound of feathers and a Great British Pound cannot be directly compared as they are measured in different units and have different physical properties.
I'm surprised by the answer GPT4 gives, and I consider it incorrect.
Since the question's context is about weight I'd expect it to consider "a Great British Pound" to mean a physical £1 sterling coin, and compare its weight (~9 grams) to the weight of the feathers (454 grams [ 1kg = 2.2lb, or "a bag of sugar" ]) .
A pound of feathers and a Great British Pound (GBP) are not directly comparable, as they represent different types of measurements.
A pound of feathers refers to a unit of mass and is equivalent to 16 ounces (or approximately 453.59 grams). It is a measure of the weight of an object, in this case, feathers.
On the other hand, a Great British Pound (GBP) is a unit of currency used in the United Kingdom. It represents a monetary value rather than a physical weight.
Thus, it's not possible to directly compare the two, as they serve entirely different purposes and units of measurement.
> Edit: GPT4 fails If I remove the sentence between (()).
If you remove that sentence, nothing indicates that you can see you picked the door with the car behind it. You could maybe infer that a rational contestant would do so, but that's not a given ...
I think that's meant to be covered by "transparent doors" being specified earlier. On the other hand, if that were the case, then Monty opening one of the doors could not result in "revealing a goat".
Why not? We should ask how the alternatives would do especially as human reasoning is machine. It’s notable that the errors of machine learning are getting closer and closer to the sort of errors humans make.
Would you have this objection if we for example perfectly copied a human brain in a computer? That would still be a machine. That would make similar mistakes
I've always found the Monty Hall problem a poor example to teach with, because the "wrong" answer is only wrong if you make some (often unarticulated) assumptions.
There are reasonable alternative interpretations in which the generally accepted answer ("always switch") is demonstrably false.
This problem is exacerbated (perhaps specific to) those who have no idea who "Monty Hall" was and what the game show(?) was... as best I can tell the unarticulated assumption is axiomatic in the original context(?).
The unarticulated assumption is not actually true in the original gameshow. Monty didn't always offer the chance to switch, and it's not at all clear whether he did so more or less often when the contestant had picked the correct door.
The assumption is that Monte will only reveal the one of the two unopened doors that has the goat behind it, as opposed to picking a door at random (which may be the car or may be the door the participant chose, which itself may or may not be the "car door").
The distinction is at which point Monte, assuming he has perfect knowledge, decides which door to reveal.
In the former, the chance to win is 2/3, in the other 1/2. However in any case, always (always meaning: in each condition, not in each repetition of the experiment, as this is irrelevant) switching is better than never switching, as there your chance to win is only 1/3.
How is it an "assumption" that Monte reveals a goat? Doesn't the question explicitly state that Monte opened one of the other two doors to reveal a goat?
Are there versions of the question where Monte doesn't reveal a goat behind his door or chooses the same door as you?
Suppose you're a contestant on a game show. You're presented with three transparent closed doors. Behind one of the doors is a car, and behind the other two doors are goats. You want to win the car.
The game proceeds as follows: You choose one of the doors, but you don't open it yet, ((but since it's transparent, you can see the car is behind it)). The host, Monty Hall, who knows what's behind each door, opens one of the other two doors, revealing a goat. Now, you have a choice to make. Do you stick with your original choice or switch to the other unopened door?
GPT4 solves it correctly while GPT3.5 falls for it everytime.
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Edit: GPT4 fails If I remove the sentence between (()).