1. The problem asks us to find the missing probability $p(4)$ in the probability distribution of the random variable $x$. 2. Recall that the sum of all probabilities in a probability distribution must equal 1. This is a fundamental rule of probability: $$\sum p(x) = 1$$ 3. Given the probabilities: $$p(0) = 0.3, \quad p(1) = 0.25, \quad p(2) = 0.2, \quad p(3) = 0.1, \quad p(4) = ?, \quad p(5) = 0.05$$ 4. We set up the equation: $$0.3 + 0.25 + 0.2 + 0.1 + p(4) + 0.05 = 1$$ 5. Combine the known probabilities: $$0.3 + 0.25 + 0.2 + 0.1 + 0.05 = 0.9$$ 6. Substitute back: $$0.9 + p(4) = 1$$ 7. Solve for $p(4)$: $$p(4) = 1 - 0.9$$ $$p(4) = 0.1$$ 8. Therefore, the missing probability $p(4)$ is 0.1. This means the probability distribution is complete and sums to 1 as required.