Question

A random number generator is used to select an integer from 1 to 3 inclusive. What is the difference between the estimated probability that a 3 is generated and the actual probability that a 3 is generated?

Answer 1

Step-by-step Answer:

In general, random number generators generate a uniform distribution, and we generally ASSUME that this is so.

If that is the case, the estimated probability of selecting a 3 is 1/3.

The actual probability depends on the generator.  Some as ASSUMED to be uniform, but it could be biased on particular numbers, knowingly or unknowingly.  

Some generators are programmed to generate particular distributions (other than uniform), such as exponential, normal, or any other probability distribution.  In these cases, the probability of selecting a 3 will depend on the distribution.

Even if the generated distribution is known, the actual probability could still be different from the theoretical (or estimated), because that is why we call them "random numbers".

In short, the "actual" probability depends on the characteristics of the generator, of which we have no knowledge.