Originally Posted by
Scorpio
something makes me think it's 2/3 since 2 out of 3 boxes has gold coins in them.
Yea, but if you had picked the box with gold-silver, and taken a gold coin, the other coin would have been silver, and we're looking for the odds that the other coin is gold too.
The correct answer, however, was indeed 2/3. Your logic was only flawed. Let me explain.
There are three boxes:
GG - gold/gold
GS - gold/silver
SS - silver/silver
Each box has an equal chance to be taken. 1/3. But that's not to the point: we can rule out the SS box, considering we have at least one gold coin.
The chance of the GS box and the SS box being taken is 1/2, right? Yes, BUT we have already opened the box and we see that it contains a gold coin. This is the clue of the riddle: the GS box has a lower chance of being the box we chose, BECAUSE THE GG BOX CONTAINS TWO GOLD COINS! The odds that the opened box WAS GG, are thus higher than the box being GS.
If the box was GS, we will not have a second gold coin.
If the box, however, was GG, we will have a second gold coin.
What are the odds? Well, let's look at just coins. There are six coins: 3S, 3G.
The GG box contains 2 of the three gold coins, the GS box contains only one of the three gold coins.
The riddle can be rephrased as "What are the odds that the first coin was one G coin from GG?". (because SS is impossible, and because GS would not have a second gold coin, and that's what we're looking for: a second gold coin. The only case that has a 'second gold coin', is the GG case.)
So there are three gold coins. GG amounts for 2 out of these three. We are looking for the GG box.
Table of possibilities
1/3: we chose G from GS
1/3: we chose G1 from GG
1/3: we chose G2 from GG
The sum of the last two is 2/3. Simple!
Bonus:
What are the odds that, by guessing randomly, you will answer
this question correctly (completely unrelated to the riddle above)?
A: 25%
B: 50%
C: 75%
D: 25%
Last edited by Arglax; Jun 22, 2014 at 12:54 PM.