1. **State the problem:** We have a Venn diagram with 100 items total. Circle A has 28 items only, circle B has 48 items only, the intersection A \cap B has 13 items, and outside both circles there are 11 items. 2. **Find P(A \cap B):** This is the probability of items in both A and B, which is the intersection number. $$P(A \cap B) = \frac{13}{100} = 0.13$$ 3. **Find P(A'):** This is the probability of items not in A. Total items not in A are those outside A, which includes items in B only (48), and outside both circles (11). Total not in A = 48 + 11 = 59 $$P(A') = \frac{59}{100} = 0.59$$ 4. **Find P(A \cup B):** This is the probability of items in A or B or both. Use the formula: $$P(A \cup B) = P(A) + P(B) - P(A \cap B)$$ Calculate P(A) and P(B): $$P(A) = \frac{28 + 13}{100} = \frac{41}{100} = 0.41$$ $$P(B) = \frac{48 + 13}{100} = \frac{61}{100} = 0.61$$ Now substitute: $$P(A \cup B) = 0.41 + 0.61 - 0.13 = 0.89$$ **Final answers:** (a) $P(A \cap B) = 0.13$ (b) $P(A') = 0.59$ (c) $P(A \cup B) = 0.89$