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IMO nowhere it is written that 1/3 of the remaining in th barrel will get emptied after a turn of the wheel. Here it is only metioned that 1/3 of the full barrel is emptied with the turn of the wheel.
So after 2 turn of the wheel, barrel will be emptied 2/3 therefore the what is left in the barrel = 1-2/3 = 1/3.
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