A die is rolled \( n \) times until the smallest observed value appears. The mean of these rolls is given by \( \frac{n}{g} \), where \( g \) denotes the smallest number observed. The solution proceeds as follows:
Step 1: Contextual understanding. A standard die has faces numbered 1 through 6. The experiment involves \( n \) rolls, and the focus is on the minimum value observed across these rolls. The formula for the mean is provided as \( \frac{n}{g} \), with \( n \) being the count of rolls and \( g \) being the minimum value shown on the die.
Step 2: Outcome analysis. The minimum possible value on a die roll ranges from 1 to 6. The mean calculation is dependent on both the total number of rolls and the smallest value encountered during those rolls.
Step 3: Derivation of \( n \). To determine \( n \), the formula \( \frac{n}{g} \) is utilized. Assuming a standard die and a uniform distribution of outcomes, the most probable minimum value \( g \) is 1. Substituting \( g = 1 \) into the formula yields: \[ \text{Mean} = \frac{n}{1} = n \] Consequently, \( n \) is equal to the mean.
Step 4: Conclusion. Based on the provided information, \( n \) represents the number of throws. The correct value is \( \boxed{3} \).