1. **State the problem:** We are given a Venn diagram with events A and B in a sample space S. We need to find the probability of the union of A and B, denoted as $P(A \cup B)$. 2. **Recall the formula:** The probability of the union of two events is given by: $$P(A \cup B) = P(A) + P(B) - P(A \cap B)$$ This formula accounts for the overlap so we don't double-count the intersection. 3. **Identify values from the diagram:** - $P(A \text{ only}) = 45$ - $P(B \text{ only}) = 15$ - $P(A \cap B) = 15$ - $P(\text{outside both}) = 25$ 4. **Calculate total sample space size:** $$|S| = 45 + 15 + 15 + 25 = 100$$ 5. **Calculate probabilities:** - $P(A) = \frac{45 + 15}{100} = \frac{60}{100} = 0.6$ - $P(B) = \frac{15 + 15}{100} = \frac{30}{100} = 0.3$ - $P(A \cap B) = \frac{15}{100} = 0.15$ 6. **Apply the formula:** $$P(A \cup B) = 0.6 + 0.3 - 0.15 = 0.75$$ 7. **Final answer:** $$\boxed{0.75}$$