This is the Bertrand's Box Paradox I read about on Wikipedia:
Assume there is three boxes:
a box containing two gold coins,
a box with two silver coins
and a box with one of each.
After choosing a box at random and withdrawing one coin at random,
if that happens to be a gold coin,
the probability is actually 66% instead of 50%.
And the problem is equivalent to asking the question
"What is the probability that I will pick a box with two coins of the same color?".
No matter how hard I try, I just couldn't comprehend this..
How is the possibility of picking a gold coin the same as the probability of picking a box with two coins of the same color?
Does this imply there is a 66% chance of picking a gold coin and a 66% chance of picking a sliver coin?
If so, can we just say there is 50% chance of picking either one of them since both stand a 66% chance....?! and suddenly everything makes no sense..
[UPDATES] It is actually the probability of the remaining coin to be gold is 66% but not the probability of obtaining the gold coin is 66%.. I've misread it....
And everything makes sense now :D !