re: Solve this OT

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There isn't a third option.

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You are confusing "option" and "possible outcome" while glossing over the context of the gold ball pick. If you know you WILL pick a gold ball, there are 3 possible outcomes, not being specific. If you HAVE PICKED a gold ball, you only have 2 possible outcomes one of which is more likely than the other based on the possibilities having chosen a gold ball.

So all of y'all can stfu now and wait for the next poster who says 50%.

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See, you don't understand the problem

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Christ almighty.

Before you choose a gold ball, how many gold balls are possible to be picked?

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How could there be 2 possible gold balls in a box with 1 ball?

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Because we don't know which ball we've picked.

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Because we don't know which ball we've picked

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yes you do. You've picked a gold one. This the remaining ball is either gold or silver. There is a 66.7 percent chance the original box you picked was the one with 2 gold balls.

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Before you pick the first gold ball, there are 3 to choose from

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Very good.

Each of those choices has a unique corresponding outcome. Period. This is what drives the probability of any given "second pull" being gold.

There is a direct one for one causal relationship between the three possible first-pulls and the three possible second-pulls.

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There is a 66.7 percent change the original box you picked was the one with 2 gold balls.

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You stop short here of what everyone else is trying to say... it's 67% because 2 of the 3 possible outcomes KNOWING that you WILL pick a gold ball reside in the first box with 2 golds.

Why are y'all all being so thick about this?

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yes you do. You've picked a gold one. This the remaining ball is either gold or silver. There is a 66.7 percent change the original box you picked was the one with 2 gold balls.

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This is slightly more enjoyable than it is annoying or else I would have given up pages ago...


We've chosen one gold ball. We know it had to come from one of two boxes, but we DON'T know which box we have yet. Those boxes contained 4 balls total. Given the fact that we don't know which box we have yet, and we've only seen one ball, there are still 3 other balls that are possibilities to be pulled out.

How someone could argue otherwise is beyond my comprehension.

The way I look at it is, if the ball comes up gold, it’s more likely that it came from the box with two gold balls, don’t you think?

You could actually replicate this experiment pretty easily. If you pull a silver ball discard that trial. If you pull gold, count how often the next ball in the box is gold vs how often it is silver. So it like 20 times and see what happens.

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So it like 20 times and see what happens.

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Not enough. You'd have to be closer to 10,000 to get close to the correct number.

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This is slightly more enjoyable than it is annoying or else I would have given up pages ago...


We've chosen one gold ball. We know it had to come from one of two boxes, but we DON'T know which box we have yet.

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you got it up to this point.

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Those boxes contained 4 balls total. Given the fact that we don't know which box we have yet, and we've only seen one ball, there are still 3 other balls that are possibilities to be pulled out

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This ignores the fact that you have preselected the box and will only pull the remaining ball from that box. They weren't all in the same box and we're paired off. Once you know you have a gold, only two options remain on your next pull.