1. **State the problem:** We have a bag with six balls labeled A, B, C, D, E, and F. We randomly pick one ball and record its letter. 2. **Sample space:** The sample space is the set of all possible outcomes when picking one ball. Since there are six balls labeled A, B, C, D, E, and F, the sample space is: $$\{A, B, C, D, E, F\}$$ 3. **Event of choosing a letter from D to F:** This event includes all outcomes where the chosen letter is D, E, or F. So the event set is: $$\{D, E, F\}$$ 4. **Summary:** - Sample space: $$\{A, B, C, D, E, F\}$$ - Event (choosing letter from D to F): $$\{D, E, F\}$$ This means when you pick a ball, it can be any of the six letters, and the event of interest is picking one of the last three letters D, E, or F.