1. The problem is to find the value of $P(2)$ given the probability mass function of a geometric distribution: $$P(x) = p(1 - p)^{x - 1}$$ where $p$ is the probability of success on any one trial. 2. To find $P(2)$, substitute $x = 2$ into the formula: $$P(2) = p(1 - p)^{2 - 1}$$ 3. Simplify the exponent: $$P(2) = p(1 - p)^1$$ 4. Since any number to the power of 1 is itself, this simplifies to: $$P(2) = p(1 - p)$$ 5. This means the probability that the first success occurs on the second trial is the probability of failure on the first trial $(1 - p)$ multiplied by the probability of success $p$ on the second trial. Final answer: $$\boxed{P(2) = p(1 - p)}$$