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There are two boxes, each with two balls. Three total balls are gold, one ball is silver.
You reach into a box at random and find a gold ball. What are the odds that the other ball from that box is one of the 2 remaining gold balls (out of 3?) 2/3.
There are one million boxes, each with two balls. One box has two gold balls, one has gold and silver, and all the rest have two silver balls.
You reach into a box at random and find a gold ball. What are the odds that the other ball from that box is one of the 2 remaining gold balls? 2/3.
In the OP scenario, there was a 1/2 (50%) chance to find the FIRST gold ball, and a 2/3 chance to find a repeat gold ball. After finding the first gold ball, it is impossible that the box you've selected has 2 silver balls, so that is removed from consideration.