Ugh, here we go.
strager wrote:
How is it different exactly?
Relevance and order. Example:
Alice holds a coin in each hand. Either coin could be either golden or silver. She holds a gold coin with the heads side face-up in her left hand. What is the probability that the other hand contains a gold coin?
Here's a list of all possible combinations.
Go = Gold, heads. Gx = Gold, tails. So = Silver, heads. Sx = Silver, tails.
Go Go
Go Gx
Gx Go
Gx Gx
Go So
So Go
Go Sx
Sx Go
Gx So
So Gx
Gx Sx
Sx Gx
So So
So Sx
Sx So
Sx Sx
Since we know the left hand holds a gold coin with heads facing up, any combination that doesn't have "Go" on the left side is impossible. This gives us a probability of 1/2. Note that the way the coin is facing is considered a relevant detail in this example. Next:
Bob holds a coin in each hand. Either coin could be either golden or silver. Bob holds a gold coin with the heads side face-up in one hand. What is the probability that the other hand contains a gold coin?
And then the combinations.
Go Go
Go Gx
Gx Go
Gx Gx
Go So
So Go
Go Sx
Sx Go
Gx So
So Gx
Gx Sx
Sx Gx
So So
So Sx
Sx So
Sx Sx
Note that "Go" can be either the left or the right coin in this example; we don't know which coin is in which hand. The probability in this case would be 3/7. This example is a simplified version of the problem in the first post. Now look at this example:
Charlie holds a coin in each hand. Either coin could be either golden or silver. Bob holds a gold coin in his left hand. What is the probability that the other hand contains a gold coin? The previously mentioned coin has the heads side facing up.
And here are the combinations:
G G
G S
S G
S S
The important thing here is
why the detail about the face-up side was given. In the first two examples, the coin in question was (presumably) picked out
because of both its material and face-up side. In this example, it was picked out only because of its material, with its face-up side being an additional detail that won't affect probability for the next pick. As for your specific example, saying "the coin was flipped on any day" is not even a detail at all.
In short, probability is a faggot, and the puzzle is basically a more advanced version of the
boy or girl paradox.
