>>13351124Ok, for the doubters that it's 2/3
Go to excel. In the first column (here starting with cell B3) make it RANDBETWEEN(1, 3). Drag it down 1000 cells or so. This represents which box we pick. (1 = 2 gold, 2 = 1 gold, 3 = 0 gold)
In the second column, enter randbetween(1, 2). This represents if we picked the gold or silver ball if we picked box 2 (1 = picked silver, 2 = picked gold)
In the third column, enter =IF(B3=1,1,IF(B3=3,0,IF(B3=2,(IF(C3=1,1,0))))). This just says: if we picked the first box, it's gold. If we picked the third box, its silver. If we picked the second box, it's gold if we picked silver and silver if we picked gold.
In the fourth column, enter =IF(B3=1,1,0). This is to check if the other ball is gold.
In the fifth column ids the result. =IF(D3=0, 3, IF(E3=1, 1, 2))
This just says, if we pick the first box, the outcome is 1 = "Gold ball picked, other ball gold". If we pick the gold in the second box, the outcome is 2 = "Gold ball picked, other ball silver". If we pick a silver, the outcome is "Silver picked"
Drag all these down 1000 cells. You will have approximately 333 outcome number 1, 167 outcome number 2, 500 outcome number 3.
So the given that a gold ball was picked (outcomes 1 and 2), the probability that the other ball is gold (outcome 1) is 2/3.
