1. **Problem:** A jar contains 8 red, 5 blue, 12 purple, and 15 yellow marbles. Find the probability of drawing: 17. a purple marble or a red marble 2. **Formula:** For "or" events (mutually exclusive), use $$P(A \text{ or } B) = P(A) + P(B)$$ 3. **Step 1:** Calculate total marbles: $$8 + 5 + 12 + 15 = 40$$ 4. **Step 2:** Calculate probabilities: $$P(\text{purple}) = \frac{12}{40}$$ $$P(\text{red}) = \frac{8}{40}$$ 5. **Step 3:** Add probabilities: $$P(\text{purple or red}) = \frac{12}{40} + \frac{8}{40} = \frac{12 + 8}{40} = \frac{20}{40}$$ 6. **Step 4:** Simplify fraction: $$\frac{20}{40} = \frac{\cancel{20}}{\cancel{40}} = \frac{1}{2}$$ **Final answer:** $$\boxed{\frac{1}{2}}$$