Statistics: Bertrand's Box Paradox [duplicate]

Possible Duplicate:
Probability problem

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 !

The result is being incompletely quoted. Perform the experiment as described. Now suppose that you end up with a gold coin. The question is: what is the probability that the other coin in the same box is gold?

This probability is $\frac{2}{3}$. Let's do an informal computation. It will be imprecise, but could be made precise by using the notion of conditional probability.

Imagine repeating the experiment $3000$ times. Then each box will be picked roughly $1000$ times. We will get a gold coin about $1500$ times. Out of these $1500$ times that we get a gold, it will have come from the two-gold box $1000$ times.

So if we restrict attention to the $1500$ times that we get a gold, about $1000$ of these times it will come from the two-gold box. So given that we got a gold coin, the probability the other coin in the same box is gold should be around $\frac{1000}{1500}$.