1. **State the problem:** We are given a discrete random variable with values $x_i = 1, 3, 7, 8$ and corresponding probabilities $p_i = 0.1, 0.4, p, 0.15$. We need to find the value of $p$. 2. **Recall the rule for probabilities:** The sum of all probabilities for a discrete random variable must equal 1. This means: $$0.1 + 0.4 + p + 0.15 = 1$$ 3. **Set up the equation:** $$0.1 + 0.4 + 0.15 + p = 1$$ 4. **Simplify the known probabilities:** $$0.65 + p = 1$$ 5. **Solve for $p$:** $$p = 1 - 0.65 = 0.35$$ 6. **Interpretation:** The value of $p$ must be 0.35 to ensure the total probability sums to 1, which matches option d). **Final answer:** $p = 0.35$