Final answer:
The concept being described is the mean or expected value, which predicts the long-term average of a discrete random variable. The correct answer is option A.
Step-by-step explanation:
The concept being described by the expected number of trips until the professor gets wet, assuming each trip has an independent chance of getting wet, is the mean or expected value. This is a fundamental concept in probability and statistics.
For example, if a professor's probability of getting wet during a trip is independent of previous trips, then by calculating the mean, we can predict how many trips, on average, the professor can expect to make before getting wet.
The mean of a probability distribution provides us with a measure of the central tendency of the distribution, while the standard deviation measures how spread out the outcomes are around the mean. In the context of this question, we're focusing on the average number of trips rather than the variability or spread of trips.