In situation where a single trial is performed and the result is determined only to be a success or failure is called a Bernoulli event. Indeed, one could create a corresponding probability function using a random variable \(X\) over the space \(R = \{0, 1 \}\) mapping \(X\)(success) = 1 and \(X\)(Failure)=0. If p = P(Success) then
\begin{equation*}
f(x) = p^x \cdot (1-p)^{1-x}
\end{equation*}
would be a formula but which only related to two values:
\begin{equation*}
P(\text{Failure}) = f(0) = (1-p)
\end{equation*}
\begin{equation*}
P(\text{Success}) = f(1) = p
\end{equation*}