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It's 1/2 if it's always gold, 2/3 if it's random. It says:
>take a ball.. at random
So it's 2/3.
>But it says "It's a gold ball"!
"Gold" does not mean "always gold". It says "random", which contradicts "always". So this interpretation is based on information which isn't there and which is contradictory to the information that is there. It's random.
>But the problem doesn't start until we've already picked the gold ball!
Doesn't matter. When dealing with questions of probability, your past random choices impact the probability of the present outcome. Your random selection of the box, for instance. You are also arbitrarily selecting a starting point. The entire statement is part of the same problem.
>But selecting the box *has* to eliminate options, selecting the ball doesn't have to eliminate possibilities!
Again this is based on nothing and contradicts the statement that the ball was randomly selected. If they wanted you to disregard your selections they would say as much instead of explicitly saying the selection was random.