Consider the situation where one can observe a sequence of independent trials where the likelihood of a success on each individual trial stays constant from trial to trial. Call this likelihood the probably of "success" and denote its value by \(p\) where \(0 \lt p \lt 1 \text{.}\) If we let the variable \(X\) measure the number of trials needed in order to obtain the rth success, \(r \ge 1\text{,}\) with \(R = \{r, r+1, r+2, ... \}\) then the resulting distribution of probabilities is called a Geometric Distribution.