There is a puzzle I read long ago and whose explanations never left me entirely satisfied.
Recently I've encountered the Boy or Girl paradox, including in particular the line:
The moral of the story is that these probabilities do not just depend on the known information, but on how that information was obtained.
I believe this may have some application to this puzzle, but I'm at a loss to see how.
Also relevant seems to be the aspect of the Monty Hall puzzle that you must be guaranteed to be shown a goat before the game starts for switching doors to have any advantage—but, again, I don't quite see the direct connection to this puzzle.
Here is the setup:
There are three cards. One card is green on both sides, one is red on both sides, and one is green on one side and red on the other.
You shuffle the cards (with your eyes closed, one would assume) and deal all three out on a table, then cover each card (with flower pots) before opening your eyes.
You uncover a single card. The visible face is green.
What are the odds that the other side of that card is green as well?
The possible answers seem to be $\frac 1 2$ and $\frac 2 3$, but I'm not sure if there are different possible assumptions/interpretations which could affect the answer.
(The "correct" answer in the book I was reading was $\frac 2 3$.)
- Under what conditions (meanings, interpretations, scenarios) would $\frac 2 3$ be the correct answer?
- In what scenarios would $\frac 1 2$ be the correct answer?
- Are there any other possible correct answers (given other interpretations)?