Suppose we start with a total of $N$ offspring of a certain animal. So we start with $N$ and no new offspring is introduced. Each year each individual of the offspring dies with probability $p$ independently.
Let $S(n$) be the first year all of the offspring is dead. Give the distribution function of $S(n)$.
My attempt: I tried to compute the probability that all the offspring is dead in the year $k$. Since for any given animal the probability that it dies in year $K$ is equal to $(1-p^k)$. Then the probability that all of them are dead is equal to $(1-p^k)^n$.
Now i don't know how to make sure $k$ was really the first year that they were all dead.
(in the my attempt part i used p as the probability an individual survives the year, i made a mistake typing the question)