Question

1. explain how empirical probability can be used to determine whether a die is “loaded” (not a fair die).

Explanation:

Empirical probability is based on actual experiments. Roll the die a large number of times. For a fair die, the theoretical probability of getting each face (1 - 6) is $\frac{1}{6}$. Compare the empirical probabilities (frequencies of each face over total rolls) with $\frac{1}{6}$. If there are significant differences, it may indicate the die is loaded.

Answer:

Roll the die many times, calculate empirical probabilities for each face value, and compare with $\frac{1}{6}$. If large discrepancies, the die may be loaded.