1. **Problem Statement:** We have a survey of 600 investors. - 380 invested in stocks. - 325 invested in bonds. - 75 did not invest in either stocks or bonds. We need to find: - How many invested in both stocks and bonds. - How many invested only in stocks. 2. **Concept:** Venn diagrams help visualize overlapping sets. Here, two sets: Stocks (S) and Bonds (B). 3. **Formula:** For two sets, $$|S \cup B| = |S| + |B| - |S \cap B|$$ where $|S \cup B|$ is the number of investors who invested in stocks or bonds or both. 4. **Calculate $|S \cup B|$:** Total investors = 600 Those who did not invest in either = 75 So, $$|S \cup B| = 600 - 75 = 525$$ 5. **Find $|S \cap B|$ (both stocks and bonds):** Using the formula, $$525 = 380 + 325 - |S \cap B|$$ $$|S \cap B| = 380 + 325 - 525 = 705 - 525 = 180$$ 6. **Find only stocks investors:** Only stocks means invested in stocks but not bonds, $$|S| - |S \cap B| = 380 - 180 = 200$$ **Final answers:** - Investors in both stocks and bonds: $180$ - Investors only in stocks: $200$