To find the expected probability for each outcome, we need to consider that each face has an equal probability of \(\frac{1}{6}\) since there are 6 faces on the cube.
Therefore, the expected probability for outcomes 2, 4, 6, 8, 10, and 12 are all \(\frac{1}{6}\).
Now, we can calculate the discrepancy for each outcome by finding the absolute difference between the experimental frequency and the expected probability.
| Outcome | Frequency | Expected Probability | Discrepancy |
|---------|-----------|-----------------------|-------------|
| 2 | 10 | \(\frac{1}{6}\) | \(|10 - \frac{1}{6}| = \frac{59}{6}\) |
| 4 | 9 | \(\frac{1}{6}\) | \(|9 - \frac{1}{6}| = \frac{53}{6}\) |
| 6 | 6 | \(\frac{1}{6}\) | \(|6 - \frac{1}{6}| = \frac{35}{6}\) |
| 8 | 15 | \(\frac{1}{6}\) | \(|15 - \frac{1}{6}| = \frac{89}{6}\) |
| 10 | 13 | \(\frac{1}{6}\) | \(|13 - \frac{1}{6}| = \frac{77}{6}\) |
| 12 | 8 | \(\frac{1}{6}\) | \(|8 - \frac{1}{6}| = \frac{47}{6}\) |
Now, we find the smallest discrepancy which is \(\frac{35}{6}\).
Converting this to a decimal rounded to the nearest thousandth, the smallest discrepancy between the experimental and expected probability is approximately 5.833.