To find out how much water had leaked out of the bucket, we can subtract the amount of water remaining from the amount of water initially in the bucket.
Initially, Sadie had \(\frac{2}{3}\) of a gallon of water. After some time, there was \(\frac{1}{3}\) of a gallon remaining.
We perform the subtraction:
\[ \frac{2}{3} - \frac{1}{3} = \frac{2 - 1}{3} = \frac{1}{3} \]
Thus, the amount of water that leaked out of the bucket is \(\frac{1}{3}\) of a gallon.