Review 1. Everleigh has 3 shirts and 2 pairs of pants in her drawer. She has 2 red shirts and a blue shirt. The pants are a pair of jeans and a pair of khakis. a. What is the probability that she picks a red shirt with khakis? b. What is the probability that she picks the blue shirt and jeans? 2. Construct a probability model for rolling a 5 -sided polyhedron. Is the probability model a uniform probability model? Explain your reasoning. 3. Determine each difference. Show your work. a. \( -9 \frac{3}{4}-10 \frac{7}{10} \) b. \( -34.9-(-71.2) \)

Sure, let's work through each of the problems step by step. --- ## 1. Probability Problems **Given:** - **Shirts:** 3 total (2 red, 1 blue) - **Pants:** 2 total (1 pair of jeans, 1 pair of khakis) ### a. Probability of Picking a Red Shirt with Khakis **Steps:** 1. **Total Possible Outcomes:** - Shirts × Pants = 3 × 2 = **6** 2. **Favorable Outcomes:** - Red Shirts × Khakis = 2 × 1 = **2** 3. **Probability Calculation:** \[ \text{Probability} = \frac{\text{Favorable Outcomes}}{\text{Total Possible Outcomes}} = \frac{2}{6} = \frac{1}{3} \] **Answer:** The probability of picking a red shirt with khakis is **\(\frac{1}{3}\)**. --- ### b. Probability of Picking the Blue Shirt and Jeans **Steps:** 1. **Total Possible Outcomes:** - Shirts × Pants = 3 × 2 = **6** 2. **Favorable Outcomes:** - Blue Shirt × Jeans = 1 × 1 = **1** 3. **Probability Calculation:** \[ \text{Probability} = \frac{\text{Favorable Outcomes}}{\text{Total Possible Outcomes}} = \frac{1}{6} \] **Answer:** The probability of picking the blue shirt and jeans is **\(\frac{1}{6}\)**. --- ## 2. Probability Model for Rolling a 5-Sided Polyhedron **Assumptions:** - The polyhedron is fair (each side is equally likely to land face up). **Probability Model Construction:** - **Possible Outcomes:** {1, 2, 3, 4, 5} - **Probability for Each Outcome:** Since there are 5 sides and the polyhedron is fair, each side has an equal probability of landing face up. \[ P(1) = P(2) = P(3) = P(4) = P(5) = \frac{1}{5} \] **Uniform Probability Model Analysis:** - A **uniform probability model** is one where all possible outcomes have the same probability. **Conclusion:** - Since each of the 5 outcomes has an equal probability of \(\frac{1}{5}\), **this is a uniform probability model**. --- ## 3. Determining Differences ### a. Calculate \( -9 \frac{3}{4} - 10 \frac{7}{10} \) **Steps:** 1. **Convert Mixed Numbers to Decimals:** - \( -9 \frac{3}{4} = -9.75 \) (Because \( \frac{3}{4} = 0.75 \)) - \( -10 \frac{7}{10} = -10.7 \) (Because \( \frac{7}{10} = 0.7 \)) 2. **Subtract the Numbers:** \[ -9.75 - 10.7 = -20.45 \] **Answer:** The difference is **\(-20.45\)**. --- ### b. Calculate \( -34.9 - (-71.2) \) **Steps:** 1. **Understand the Operation:** - Subtracting a negative is the same as adding the positive. 2. **Convert the Expression:** \[ -34.9 - (-71.2) = -34.9 + 71.2 \] 3. **Perform the Addition:** \[ -34.9 + 71.2 = 36.3 \] **Answer:** The difference is **\(36.3\)**. --- If you have any further questions or need additional clarification on any of these problems, feel free to ask!