>>14014661Your intuitive explanation doesn't make sense.
The question asks what is the probability that the SECOND ball from the SAME box is gold. You can only draw a silver ball from the third box therefore we can ignore it completely as our condition is that a gold ball was already drawn.
That leaves two boxes. If silver ball 1 is drawn then the trial is rerun as a gold ball was not drawn. Therefore the only trials that count are when gold balls g1, g2, or g3 are drawn.
If g1 is drawn, the 2nd ball drawn from the same box will be gold.
If g2 is drawn, the 2nd ball from the same box will be gold.
If g3 is drawn, the 2nd ball from the same box will be silver.
The probability of drawing one of the three gold balls is 1/3 for each.
The case when the next ball will be gold only occurs when drawing g1 or g2 so the probability of the next ball being gold =P(g1) + P(g2) = 1/3 + 1/3 = 2/3
>t. brainlet 
