1. **Stating the problem:** Calculate the probabilities for the sets D (Denmark), C (Canada), and R (Russia) based on the given Venn diagram counts. 2. **Total number of elements:** Sum all numbers inside and outside the circles: $$32 + 18 + 7 + 7 + 3 + 4 + 4 + 25 = 100$$ 3. **Calculate each probability:** - $P(R)$: Sum of all elements in circle R: $$7 + 3 + 4 + 4 = 18$$ - $P(C)$: Sum of all elements in circle C: $$18 + 7 + 3 + 4 = 32$$ - $P(D)$: Sum of all elements in circle D: $$32 + 18 + 7 + 3 = 60$$ - $P(D)'$: Complement of $P(D)$: $$1 - P(D) = 1 - \frac{60}{100} = \frac{40}{100} = 0.40$$ - $P(D \cap C)$: Intersection of D and C: $$18 + 3 = 21$$ - $P(D \cup C \cup R)$: Union of all three sets is the total inside all circles: $$32 + 18 + 7 + 7 + 3 + 4 + 4 = 75$$ - $P(D \cap C \cap R)$: Intersection of all three sets: $$3$$ - $P((D \cup C \cup R)')$: Complement of union: $$1 - \frac{75}{100} = \frac{25}{100} = 0.25$$ - $P(D \cup C)'$: Complement of union of D and C: Union of D and C is: $$32 + 18 + 7 + 3 = 60$$ Complement: $$1 - \frac{60}{100} = 0.40$$ - $P((D \cap C \cap R)')$: Complement of intersection of all three: $$1 - \frac{3}{100} = 0.97$$ 4. **Convert counts to probabilities by dividing by total 100 and round to 2 decimals:** $$P(R) = \frac{18}{100} = 0.18$$ $$P(C) = \frac{32}{100} = 0.32$$ $$P(D) = \frac{60}{100} = 0.60$$ $$P(D)' = 0.40$$ $$P(D \cap C) = \frac{21}{100} = 0.21$$ $$P(D \cup C \cup R) = \frac{75}{100} = 0.75$$ $$P(D \cap C \cap R) = \frac{3}{100} = 0.03$$ $$P((D \cup C \cup R)') = 0.25$$ $$P(D \cup C)' = 0.40$$ $$P((D \cap C \cap R)') = 0.97$$