>>515289787
I literally write logic for this sort of shit for a living, and wrote one of the counter-encryption algorithms my country uses for a particular process, absolutely smashing what was thought to be the compute complexity of the problem.
Using fourths there makes perfect sense - but let's go back and use sixths to make it fucking clearer for you.
There are 3 boxes of equal chance - 1/3 each. In each box is 2 balls of 1/2 chance, meaning each ball is 1/6
3 of those 1/6 chances are gold, so represent 100% of the cases we care about, which are equal, so each ball represents 1/3 of the selection options, and only 1 ball is correct, so 1/3 total.
If you eliminate the S+S box, that 1/3 * 1/2 = 1/6 becomes 1/2 * 1/2 or 1/4 chance for each remaining ball, of which 3/4 are gold. Fourths makes perfect sense.
If you replace the 2 gold balls in the first box with 100 gold balls, and the 2 silver balls with 100 silver balls, nothing changes in the end, but the calculations slightly change - both the first and last box are still 1/3, but in the first and last box the chance of any 1 ball is now 1/100 - with a 1/3 chance in each box 1/3 * 1/100 = 1/300, times 100 balls is 100/300 or 1/3.
So you have a 1/3 chance of a gold ball from box 1, and a 1/6 chance of a gold ball from box 2: 1/3 + 1/6 = 3/6. If we have a 3/6 chance of picking a gold ball still, and only 1/6 chance of it being the correct gold ball for the other ball to be silver, that's still 1/3, the answer doesn't change.
If you can't see that in your head, just draw the decision tree on paper so your NPC ass can understand without a inner voice like those of us with souls have.