/sci/ - Science & Math

>>9471927
Also, think about it from the perspective of if the reverse were true, that choosing a silver after a gold were 1/2 instead of 1/3. How can there possibly be a 1/2 chance of this?

The essence is that it is tempting to think that the silver-silver box can be simply ignored, because it contains no gold balls. However, this is not the case; it is very important to the problem. The fact is, there are three gold balls which can be selected. The gold-gold box has twice the chance of being chosen.
>but it's not a MAGIC box!!!1!
No, but because we know that the first ball chosen is gold, there are three possibilities for the second choice, a gold, a gold, and a silver. The probability for the second choice being gold IS 2/3.

I have also attached my Python program which simulates many trials of this exact experiment. The result was:

0.666634227027

If you don't bother to take a break from this and come back with a fresh perspective, then I am not sure how to help you. Try not to get emotional.