1. **State the problem:** We are given a Venn diagram with events A and B in a sample space S with equally likely outcomes. We need to find the probability $P(A' \cup B)$, where $A'$ is the complement of A. 2. **Recall the formula:** The probability of the union of two events is given by $$P(A' \cup B) = P(A') + P(B) - P(A' \cap B).$$ 3. **Understand the complement:** The complement $A'$ consists of all outcomes not in A. 4. **Identify the counts from the diagram:** - $|A \text{ only}| = 45$ - $|A \cap B| = 10$ - $|B \text{ only}| = 20$ - $|\text{outside both}| = 25$ 5. **Calculate total sample space size:** $$|S| = 45 + 10 + 20 + 25 = 100.$$ 6. **Calculate $P(A')$:** $A'$ includes outcomes outside A, which are $B \text{ only} + \text{outside both} = 20 + 25 = 45$. $$P(A') = \frac{45}{100} = 0.45.$$ 7. **Calculate $P(B)$:** $B$ includes $A \cap B$ and $B \text{ only}$, so $$P(B) = \frac{10 + 20}{100} = \frac{30}{100} = 0.30.$$ 8. **Calculate $P(A' \cap B)$:** $A' \cap B$ is the part of B not in A, which is $B \text{ only} = 20$. $$P(A' \cap B) = \frac{20}{100} = 0.20.$$ 9. **Calculate $P(A' \cup B)$:** $$P(A' \cup B) = P(A') + P(B) - P(A' \cap B) = 0.45 + 0.30 - 0.20 = 0.55.$$ **Final answer:** $$\boxed{0.55}$$