math.randomseed(os.time()) -- ignore this
local TESTS = 1000000 -- how many tests are done
local SPECKS_PER_BOX = 10000 -- how many specks of dust get put in each box
local boxes = {
    [1] = {}, -- gold dust
    [2] = {}, -- silver with gold speck
    [3] = {}  -- silver dust
}

-- Put the specks of gold into the box
for i = 1, SPECKS_PER_BOX do -- do this SPECKS_PER_BOX times
    table.insert(boxes[1], "g") -- put a speck of gold dust into the gold dust box
    table.insert(boxes[2], "s") -- put a speck of silver dust into the silver dust with gold speck box
    table.insert(boxes[3], "s") -- put a speck of silver dust into the silver dust box
end
-- each box now has SPECKS_PER_BOX specks of corresponding dust in it

-- now, at random, we replace one of the silver specks in the "silver dust with gold speck" box with a gold speck
boxes[2][math.random(1,SPECKS_PER_BOX)] = "g"

-- now, we simulate the question
local restOfBoxWasGold = 0
local goldSpecksChosen = 0
for i = 1, TESTS do -- do everything in this block TESTS times
    local chosenBox = boxes[math.random(1, 3)] -- You pick a box at random,
    local chosenSpeck = chosenBox[math.random(1, #chosenBox)] -- then pick a random speck of dust from that box.
    if chosenSpeck == "g" then -- Given that you chose a gold speck,
        -- what is the probability that the rest of the box is gold?
        if chosenBox == boxes[1] then
            restOfBoxWasGold = restOfBoxWasGold + 1
        end
        goldSpecksChosen = goldSpecksChosen + 1
    end
end

print("Probability: " .. restOfBoxWasGold/goldSpecksChosen * 100 .. "%")