holy shit 66%

...

But there's only two boxes, third one doesn't exist for the problem

fixed

how did i do?

P[gg | one g] = P[gg] / P[one g] = 1/3 / 1/2 = 2/3

Yeah, no:
en.wikipedia.org/wiki/Bertrand's_box_paradox#Solution

>le troll face
nest those if statments fuckface

>No. They are functionally identical
No they're not and you're only asserting they are because you know you answered the wrong question.

Correct.

Imagine the Gold Balls are labeled A, B, C, D, E and F.

You got a gold ball with the first pick. Can't be E or F, because there's no chance of getting a gold ball there.

Your first pick must be A, B or C. It wasn't D.

If you picked A, your next is B.
If you picked B, your next is A.
If you picked C, your next is D.

2/3 of B, A and D are Golden. 66%.

And I don't even fucking know math.

>nest those if statments fuckface
That would answer the wrong question. If you're ever considering the probability of pulling out the initial gold then it means your answer is wrong.