What I am looking for now is the name of the distribution that describes the situation of exactly $k$ successes in a row of random events of probability $p$.
To give an example, if $k = 3$, that would be the chance that you subsequently throw heads 3 times and then throw tails. If I'm not mistaken (please correct me if I'm wrong), the probability reads as:
$$ P(k, p) = p^k (1-p) $$
It's a pretty simple distribution that I'm sure I've come across in class one day, I'm just wondering for its name.
Pro question:
A related distribution is the distribution in which you have $N$ trials, and you're looking for exactly $k$ subsequent successes (obviously $k \leq N$ ) of a random event with probability $p$. So it's much like a binomial distribution but for subsequent events. Does this distribution have a name?