1. **State the problem:** We are given the probability mass function (PMF) of a geometric distribution: $$P(x) = p(1-p)^{x-1}$$ and asked to find $$P(4)$$ for a given probability $$p$$. 2. **Recall the formula:** The PMF of a geometric distribution is $$P(x) = p(1-p)^{x-1}$$ where $$p$$ is the probability of success on each trial and $$x$$ is the trial number of the first success. 3. **Substitute $$x=4$$ into the formula:** $$P(4) = p(1-p)^{4-1} = p(1-p)^3$$ 4. **Interpretation:** This means the probability that the first success occurs on the 4th trial is the probability of failure in the first 3 trials ($$(1-p)^3$$) multiplied by the probability of success on the 4th trial ($$p$$). 5. **Final answer:** $$P(4) = p(1-p)^3$$