1. **State the problem:** We are given that 25 states have four-star hotels out of a total of 50 states. We need to find: (a) The fraction of states with at least one four-star hotel. (b) The number of states without a four-star hotel. (c) The fraction of states without a four-star hotel. 2. **Formula and rules:** - Fraction of states with four-star hotels = \frac{\text{number of states with hotels}}{\text{total number of states}}. - Number of states without hotels = total states - states with hotels. - Fraction of states without hotels = \frac{\text{number of states without hotels}}{\text{total number of states}}. 3. **Calculate fraction of states with four-star hotels:** $$\frac{25}{50}$$ Simplify by dividing numerator and denominator by 25: $$\frac{\cancel{25}}{\cancel{50}} = \frac{1}{2}$$ So, the fraction is $\frac{1}{2}$. 4. **Calculate number of states without four-star hotels:** $$50 - 25 = 25$$ So, 25 states do not have a four-star hotel. 5. **Calculate fraction of states without four-star hotels:** $$\frac{25}{50}$$ Simplify by dividing numerator and denominator by 25: $$\frac{\cancel{25}}{\cancel{50}} = \frac{1}{2}$$ So, the fraction is $\frac{1}{2}$. **Final answers:** (a) $\frac{1}{2}$ (b) 25 states (c) $\frac{1}{2}$