a - A pair of dice is thrown 11 times. What is the probabiliy that the eleven possible values of their sum are obtained once each (this can be solved by simple probability theory).
b - if the pair of dice is thrown 12 times, what is the probability that the eleven possible values of their sum are obtained at least once each
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
A number by itself is useful, but it is far more useful to know how accurate or certain that number is.