In a trial, the probability of failure is $p$. If the trial is repeated $n$ times, the probability of failure is $p^n$. That is, if the trial is performed 2 times, the probability of failure is $p^2$; if performed 3 times the probability of failure is $p^3$.
I want to know, what is the probability distribution of the trials?
Edit: Well, I have two questions in mind.
- What is the probability that there is a failure after $n$ trials? The answer is:
$1-(1-p)^n$
- What is the probability that there is a success after $n$ trials? The answer is:
$1-p^n$
What are these distributions?