First pick: 1/3 chance of picking each box. Chance of picking a gold ball is then 1/3 for box 1 + 1/6 for box 2 since if box 2 is chosen, half the time you get gold.
Knowing that you draw gold on the first pick, the odds that you drew from box 1 is therefore 2/3, and the odds that you drew from box 2 is 1/3.
Therefore the 2nd draw has a 2/3 chance to be gold.
