1. **State the problem:** Laura rolled a number cube 500 times with outcomes 1 through 6 and recorded the number of rolls for each outcome. We need to find: (a) The experimental probability of rolling a 5 or 6. (b) The theoretical probability of rolling a 5 or 6 assuming the cube is fair. (c) Choose the true statement about the difference between experimental and theoretical probabilities with a large number of rolls. 2. **Recall the formulas:** - Experimental probability of an event = \( \frac{\text{Number of times event occurs}}{\text{Total number of trials}} \) - Theoretical probability of an event = \( \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} \) 3. **Calculate the experimental probability of rolling a 5 or 6:** - Number of rolls for 5 = 97 - Number of rolls for 6 = 83 - Total rolls = 500 \[ \text{Experimental probability} = \frac{97 + 83}{500} = \frac{180}{500} \] Simplify the fraction: \[ \frac{180}{500} = \frac{\cancel{180}}{\cancel{500}} = \frac{36}{100} = 0.36 \] Rounded to the nearest thousandth: \(0.360\) 4. **Calculate the theoretical probability of rolling a 5 or 6:** - Number of favorable outcomes = 2 (5 and 6) - Total possible outcomes = 6 \[ \text{Theoretical probability} = \frac{2}{6} = \frac{\cancel{2}}{\cancel{6}} = \frac{1}{3} \approx 0.333 \] Rounded to the nearest thousandth: \(0.333\) 5. **Choose the true statement:** - With a large number of rolls, there might be a difference between the experimental and theoretical probabilities, but the difference should be small. This is because experimental probability approaches theoretical probability as the number of trials increases, but small differences can still occur due to chance. **Final answers:** (a) Experimental probability = \(0.360\) (b) Theoretical probability = \(0.333\) (c) True statement: "With a large number of rolls, there might be a difference between the experimental and theoretical probabilities, but the difference should be small."