Option #2: No, her sample is not an appropriate, random sample. It does not represent the whole population.
Explanation: Testing only 15 ice samples from randomly selected coffee drinks may not accurately represent the entire population of ice used in the coffee shop, especially given the shop sells around 500 cups a day. The sample size is relatively small compared to the total number of coffee drinks served daily, and various factors like the timing of the samples, different types of drinks ordered, or changes in ice handling could influence the cleanliness of the ice. A larger, more systematic sampling approach would provide a better representation of the ice quality.