Question:
In front of me is a shuffled deck of cards. I turn over cards until I reach the first Ace. I discard all these cards, and then turn over one more and place it face up. Which card are we more likely to see: the Ace of Diamonds, or the Queen of Clubs?
Answer:
They have the same probability.
Resolution Criteria: Most people think: well if I draw a card randomly from the deck they have equal chance. But here, I know I've turned over at least one ace, and it might have been the Diamonds, in which case it couldn't be the next card. So the queen should be more likely. But on the other hand maybe because the Queen might have been discarded before even drawing the first ace that makes the Aces more likely! It turns out these two basically magically cancel each other out.
As for GPT-4, I won't judge the model's proof or argument. I just want it to say that the they're equally likely, even if the logic is wrong.
As for GPT-4, I won't judge the model's proof or argument. I just want it to say that the they're equally likely, even if the logic is wrong.