A probability word problem, it's not a riddle, no trick answer. You have 3 identical boxes. One contains 2 gold marbles, one 2 silver marbles, one 1 of each. You can't look in the boxes. You pick one of the boxes at random. You reach in and pull out a gold marble. What are the odds the second marble you pull out of the box will be gold?

Having drawn a gold marble first, it's more likely that you selected the gold-gold box.

@cmadler But in my careful reading of the question you are not selecting the other box. That would make the problem more interesting. Then it might be the Monte Hall problem that I referenced earlier.

[mathworld.wolfram.com]

@marmot84 On the initial draw there are six possibilities (six marbles). You had two chances at drawing gold from the gold-gold box, two chances at drawing silver from the silver-silver box, one chance of drawing gold from the mixed box, and one chance of drawing silver from the mixed box.

Once you make your first draw and get gold, you've eliminated three of those possibilities and have three left. You have either drawn gold from the gold-gold box (two chances) or gold from the mixed box (one chance). So there is a 2/3 chance you'll get gold on the second draw.

@cmadler Oh! I see your line of reasoning. Have to pause to think about it though because I think I have an objection...

Ok... yes, you are correct. Wow! Probabilities are often counter-intuitive and being an intuitive thinker I tend to try that first. Definitely, I'm wrong in this case! Cool!