1. **Problem statement:** Ricardo has 6 pairs of socks, each pair a different color: red, brown, green, white, black, and blue. He reaches into the drawer to get one pair. We analyze the possible outcomes and probabilities. 2. **Number of possible outcomes:** Since there are 6 distinct pairs, the number of possible outcomes is simply the number of pairs. $$\text{Number of outcomes} = 6$$ 3. **Possible outcomes:** The possible outcomes are the colors of the pairs he can pick: red, brown, green, white, black, blue 4. **Sample space:** The sample space $S$ is the set of all possible outcomes: $$S = \{\text{red}, \text{brown}, \text{green}, \text{white}, \text{black}, \text{blue}\}$$ 5. **Calculate $P(\text{blue})$:** Probability of picking the blue pair is the number of favorable outcomes over total outcomes: $$P(\text{blue}) = \frac{1}{6}$$ 6. **Calculate $P(\text{green})$:** Similarly, $$P(\text{green}) = \frac{1}{6}$$ 7. **Calculate $P(\text{not red})$:** Probability of not picking red is total outcomes minus red outcomes over total outcomes: $$P(\text{not red}) = \frac{6 - 1}{6} = \frac{5}{6}$$ 8. **Calculate $P(\text{not purple})$:** Since purple is not in the drawer, the probability of not picking purple is 1 (certain event): $$P(\text{not purple}) = 1$$ **Final answers:** - Number of possible outcomes: 6 - Sample space: $\{\text{red}, \text{brown}, \text{green}, \text{white}, \text{black}, \text{blue}\}$ - $P(\text{blue}) = \frac{1}{6}$ - $P(\text{green}) = \frac{1}{6}$ - $P(\text{not red}) = \frac{5}{6}$ - $P(\text{not purple}) = 1$