re: Solve this OT

I retract my 50% answer.

It takes a big man to admit when he is wrong.

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Well that is the reality. You are pulling 1 remaining ball from a box, it only has 2 possible outcomes.

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Under the parameters you're setting, that's true. You're saying it can only be gold or silver. That's accurate.

We're saying it will be one of THREE unknown balls (outcomes) that remain for each of the possible original choices.

Your explanation and refusal to acknowledge the three outcomes is the same logic people use to say you either chose box 1 or box 2, so he answer is 50%. The reality of the situation is that your gold ball was one of 3 possible choices. Those 3 choices each have a distinct resolution, and those resolutions are why the answer is 67%.

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And 1 divided by 2 is.....

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How many brains you have.

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Because it is 66.7% more likely you pulled a gold ball from a box with 2 gold balls than a box with 1 gold ball.

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This is handwaving the statistics and regurgitating the answer.

Explain to me why.

Here I'll help... In the analogy you posted the probability is substantially different:

Your probability of picking the gold from the majority silver box is 1/51 = 1.96%

Given a random selection of gold, your probability of picking another gold from the same box is 98.04% (50/51).

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I'm gonna agree with PearlJam's nuance.
You guys seem to put an emphasis in it being possibly a different ball. The emphasis should be on the fact that there were two of them in that box making it more likely to have come from that box.

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Exactly

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ou can't pull G1 or G2 with you second pick. Either 1 of them is in your hand and out of play or they are both in the box you didn't select.

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Yes you can. The labels are how they go into the box, not what you assign to them after you've chosen one.

Go back to my human box analogy. Your first pick is a male. That means you either picked John, James, or Jack. If you picked John, the next pick is James. If you picked James, the next pick is John. If you picked Jack, the next pick is Jill. We don't know who you picked, just that he's a male. As a result, there are still 3 (three) possible people that will come out of the box. Two of them are male, one of them is female.

If you'd like to say there are two possible sexes that can come out of the box, that's also true.

I am trying to think of a way using combinations:

Eliminating the obvious now [S,S] and adding the fact you have successfully chosen a G ball, You are left 3 choose 1 combinations (3 comb) in two boxes: [G1,G2], [G3,S].

The combinations are:

G1,G2
G2,G1
G3,S

2 out of the 3 combinations (67%) grant you a successful outcome.

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You guys seem to put an emphasis in it being possibly a different ball. The emphasis should be on the fact that there were two of them in that box making it more likely to have come from that box.

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If you can agree that you picked one of 3 possible gold balls, I can't fathom how you can disagree with the fact that you have one of 3 possible outcomes.

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Once you have the gold ball in hand, the next ball is one of the 3 remaining balls we haven't seen.

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Uhhh... It is either silver or gold. They aren't all in the same box and a gold ball has been eliminated. It's either the gold ball that was in the box with a silver ball or it is one of the 2 gold balls that were once together.