>>7981072Define the box with two gold balls as box A, one silver one gold as box B, two silver as box C.
Box A contains balls 1 (gold) and 2 (gold), box B 3 (gold) and 4 (silver), box C 5 (silver) and 6 (silver).
There are 6 possibilities at the start.
You select:
1. Box A, then ball 1. You are holding a gold ball, there is another gold ball in your box.
2. Box A, then ball 2. You are holding a gold ball, there is another gold ball in your box.
3. Box B, then ball 3. You are holding a gold ball, there is a silver ball in your box.
4. Box B, then ball 4. You are holding a silver ball, there is a gold ball in your box.
5. Box C, then ball 5. You are holding a silver ball, there is another silver ball in your box.
6. Box c, then ball 6. You are holding a silver ball, there is another silver ball in your box.
Now, because we've limited you to only selecting a gold ball, we can eliminate all outcomes that result you drawing a silver ball.
So now the possible outcomes are:
1. Box A, then ball 1. You are holding a gold ball, there is another gold ball in your box.
2. Box A, then ball 2. You are holding a gold ball, there is another gold ball in your box.
3. Box B, then ball 3. You are holding a gold ball, there is a silver ball in your box.
Three outcomes, two of which are form box A. 2/3 chance that you've drawn a box A ball.
