Final answer:
The question requires the application of probability and statistics to determine the likelihood of a certain number of simultaneous events occurring, which could be addressed using the Poisson or exponential distributions depending on the context.
Step-by-step explanation:
The question asks to find the probability that at any given time, exactly n users are transmitting simultaneously. This is a typical problem in the field of probability and statistics, particularly dealing with stochastic processes or random variables that can be modeled using distributions such as the Poisson or binomial distributions.
For instance, we could use the Poisson distribution to model the number of events occurring within a fixed interval when these events happen with a known average rate and independently of the time since the last event. In the scenario where we are interested in finding the probability that fewer than 20 calls occur within an hour, assuming we know the average rate of calls per hour, we can apply the Poisson distribution formula to calculate this probability.
Similarly, to find the probability of time intervals between successive events (like calls or customer arrivals), we might use exponential distribution, especially if we are interested in properties like the 'memoryless property' which indicates that the probability of an event occurring in the next interval is independent of how much time has already elapsed.