
Coupon collector's problem - Wikipedia
https://en.m.wikipedia.org/wiki/Coupon_collector%27s_problem

probability - Expected time to roll all $1$ through $6$ on a die - Mathematics Stack Exchange
https://math.stackexchange.com/questions/28905/expected-time-to-roll-all-1-through-6-on-a-die

https://en.wikipedia.org/wiki/Geometric_distribution?wprov=sfti1#


Geometric distribution

Consider a sequence of independent trials, where each trial has only two possible outcomes (designated failure and success). The probability of success, p, is assumed to be the same for each trial. In such a sequence of trials, the geometric distribution is useful to model the number of failures before the first success since the experiment can have an indefinite number of trials until success

The geometric distribution gives the probability that the first occurrence of success requires k independent trials, each with success probability p . If the probability of success on each trial is p , then the probability that the k-th trial is the first success is

Pr(X=k)=(1-p)^{k-1}p

for k = 1 ,2 ,3 ,4 , ...

The Coupon Collectors problem can also be modeled using geometric random variables. 

A geometric random variable has the following properties:  Expectation: E(X) = 1/p  
Variance: Var(X) = (1-p)/p^2