Scenario A: In a game, every time you beat a boss, you have a chance of receiving a drop. The base drop rate at zero wins is $1.5$%. This drop rate increases by $0.5$% after each win. So, your chance of receiving a drop on your second win is $2.0$%. Cumulatively, your chance of earning the drop by $2$ WINS is $3.47$%.
Each boss has multiple drops, however. Let's say a boss has two drops. Each drop has the same drop rate as described above and rolls individually. So, you can get both drops in one run, one drop, or zero drops.
What is the probability that by $10$ runs, you will have earned both drops? Optionally, how would you put this in a simple formula in Excel where you can vary $X$ where $X$ is number of runs?
Scenario B: What if there was a situation where there were two drops but with different rarities. One drop has the drop rate described in Scenario $A$ ($1.5$% base increasing by $0.5$% after each win) and another drop is rarer and has the base drop rate of $0.5$% but increases by $0.1$% after each win? What is the probability that by $10$ runs, you will have earned both drops?
Let's say you have $n$ drops named $d_1,d_2,...,d_n$ respectively having bases $b_1,b_2,...,b_n$ and increasing rates $i_1,i_2,...,i_n$, such that drop $d_k$ has probability $b_ki_k^{\space j}$ after $j$ wins to be recived. For drop $d_k$ the probability $P(d_k)$ to be recived after $r$ runs is the complement to the probability of failing at each run so $P(d_k)=1-\displaystyle\prod_{j=0}^{r-1} 1-b_ki_k^j \space$.
Since the drops are indipendent from each other the probability of winning a set of the $n$ drops is the product of the probabilities to win each drop included in the set and the probabilities to lose each drop not included.