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 first success with \(R = \{1, 2, 3, ... \}\text{,}\) then the resulting distribution of probabilities is called a Geometric Distribution.