1. The problem is to find the value of $P(4)$ given the function $P(x) = p(1 - p)^{x-1}$. 2. This function is a geometric probability mass function where $p$ is the probability of success and $x$ is the trial number. 3. To find $P(4)$, substitute $x=4$ into the formula: $$P(4) = p(1 - p)^{4-1} = p(1 - p)^3$$ 4. This expression means the probability of the first success occurring on the 4th trial is $p$ times the probability of failure $(1-p)$ raised to the power of 3. 5. Without a specific value for $p$, this is the simplified expression for $P(4)$. Final answer: $$P(4) = p(1 - p)^3$$