How many papers do you expect to hand in before you receive each possible grade at least once? [duplicate]

A particular professor is known for his arbitrary grading policies. Each paper receives a grade from the set {A, A-, B+, B, B-, C+}, with equal probability, independently of other papers. How many papers do you expect to hand in before you receive each possible grade at least once?

Solution 1:

If a series of independent events each have probability $p$, then the expected duration until the first occurrence is $$ \begin{align} &1\overbrace{p}^{\text{$1$ success}}+2\overbrace{(1-p)p}^{\begin{array}{l}\text{$1$ failure}\\\text{$1$ success}\end{array}}+3\overbrace{(1-p)^2p}^{\begin{array}{l}\text{$2$ failures}\\\text{$1$ success}\end{array}}+4\overbrace{(1-p)^3p}^{\begin{array}{l}\text{$3$ failures}\\\text{$1$ success}\end{array}}+\dots\\ &=\sum_{k=1}^\infty k\color{#C00000}{p}\color{#00A000}{(1-p)}^{k-1}\\ &=\frac{\color{#C00000}{p}}{(1-\color{#00A000}{(1-p)})^2}\\ &=\frac1p \end{align} $$ The probability of getting a new grade after you have already gotten $k$ grades is $\frac{6-k}{6}$.

Thus, the expected duration to get your first new grade is $\frac66$; the expected duration to get your second new grade is $\frac65$; the expected duration to get your third new grade is $\frac64$; etc.