1. **Problem 1: Probability Sam's brother did not choose the correct card** A standard deck has 52 cards. The probability of choosing the correct card is $\frac{1}{52}$. The probability of not choosing the correct card is the complement: $$P(\text{not correct}) = 1 - P(\text{correct}) = 1 - \frac{1}{52}$$ 2. Simplify the expression: $$1 - \frac{1}{52} = \frac{52}{52} - \frac{1}{52} = \frac{52 - 1}{52} = \frac{51}{52}$$ 3. Therefore, the probability that Sam's brother did not choose the correct card is $\frac{51}{52}$. --- 1. **Problem 2: Complement of Victor pulling an emerald stone** Victor has 8 stones: 5 emerald and 3 ruby. The probability of pulling an emerald stone is: $$P(\text{emerald}) = \frac{5}{8}$$ The complement is pulling a stone that is not emerald, which means pulling a ruby stone: $$P(\text{not emerald}) = 1 - P(\text{emerald}) = 1 - \frac{5}{8}$$ 2. Simplify the expression: $$1 - \frac{5}{8} = \frac{8}{8} - \frac{5}{8} = \frac{8 - 5}{8} = \frac{3}{8}$$ 3. Therefore, the complement of pulling an emerald stone is $\frac{3}{8}$. **Final answers:** - Problem 1: $\frac{51}{52}$ (Option C) - Problem 2: $\frac{3}{8}$ (Option B)