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Notes -
In that case, since we know he drew one gold coin, it also rules out Box 1, so we’re left with Box 2 and 3. We know that initially there were 13 coins here (3 gold, 10 silver) so now there are 12 coins left (2 gold, 10 silver). So 2 gold out of 12 remaining coins = 1 in 6 chance = 16.66%?
[Of course, the chances of him plucking a gold coin in the first place would have been much less than the 50% in the first question – it would actually have been just 20% 2 silver 2 gold 1 gold, 10 silver = 3 gold vs 12 silver = 20% But since we know he did actually pick a gold coin first, the chances of him also picking a gold coin second are 16.66%.]
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