We can suppose that we have $n$ processes, each with the same parameters. Further, each successive process is allowed to start only after the previous process has completed.
Now, a process completes with probability $1-(1/2)^t$ at time $t$. In other words, the process always has a 50-50 chance of completing at time $t+1$, if it did not complete at time $t$.
I'm wondering two things. What function gives the probability that $n$ of these processes will complete at time $t$? Also, if we have the time $t$, what is the probability that $n$ processes have completed?