>>23318402
>>23318034
If you performed the experiment in real life, making each choice randomly, it would boil down to the fact that there are six "paths" through the process.

There are three paths through that involve drawing a gold ball first. At the end of two of these paths is another gold ball, while at the end of only one of them is a silver ball.

If both choices are Random as the question states, then all six paths are equally likely, and all three gold-first paths equally likely to each other. That is why it's thirds.