1. Problem 28: Find the probability that a randomly selected registered voter in Belair will vote for the Democratic candidate. 2. Formula: Probability $P = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$ 3. Given: Number of voters = 350, voters for Democratic candidate = 123 4. Calculate probability: $$P = \frac{123}{350}$$ 5. Simplify fraction: $$P \approx 0.3514$$ 6. Interpretation: There is about a 35.14% chance a randomly selected voter will vote Democratic. --- 7. Problem 29: Probability of drawing tickets with various discounts from a box. 8. Total tickets = 3000 + 500 + 100 + 1 = 3601 9. (a) Probability of 100% discount: $$P = \frac{1}{3601} \approx 0.00028$$ 10. (b) Probability of 50% discount: $$P = \frac{100}{3601} \approx 0.0278$$ 11. (c) Probability of less than 50% discount means 10% or 30% discount tickets: $$P = \frac{3000 + 500}{3601} = \frac{3500}{3601} \approx 0.9728$$ --- 12. Problem 29(c) Hispanic activity participation: Can we add male and female percentages? 13. No, because percentages are relative to each gender group, not the whole Hispanic population. 14. To find overall Hispanic participation, weighted average based on population sizes of males and females is needed. --- 15. Problem 33: Sample space of blood types with Rh factor. 16. Blood types: A, B, AB, O 17. Rh factor: + or - 18. Sample space: $$\{A+, A-, B+, B-, AB+, AB-, O+, O-\}$$ 19. This is not equiprobable because frequencies of blood types and Rh factors vary in populations. --- 20. Problem 34: Equiprobable sample space for 3 children gender combinations. 21. Each child can be Male (M) or Female (F), so total outcomes: $$2^3 = 8$$ 22. Sample space: $$\{MMM, MMF, MFM, MFF, FMM, FMF, FFM, FFF\}$$ 23. Each outcome is equally likely assuming equal probability of male or female births. --- 24. Problem 35: Probability of type AB blood. 25. Given: 4% have AB blood. 26. (a) Probability of AB blood: $$P = 0.04$$ 27. (b) Probability of not AB blood: $$P = 1 - 0.04 = 0.96$$ --- 28. Problem 36: Probability of Rh factor. 29. Given: 16% negative Rh, 84% positive Rh. 30. (a) Probability negative Rh: $$P = 0.16$$ 31. (b) Probability positive Rh: $$P = 0.84$$ --- 32. Problem 37: Probability of Asian descent in Los Angeles. 33. Given: 10% Asian descent. 34. (a) Probability Asian descent: $$P = 0.10$$ 35. (b) Probability not Asian descent: $$P = 1 - 0.10 = 0.90$$ --- 36. Problem 38: Probability of Hispanic descent in Houston. 37. Given: 37.4% Hispanic descent. 38. (a) Probability Hispanic descent: $$P = 0.374$$ 39. (b) Probability not Hispanic descent: $$P = 1 - 0.374 = 0.626$$ --- 40. Problem 39: Probability of empty capsule. 41. Given: 2,000,000 capsules, 60,000 empty. 42. Probability empty capsule: $$P = \frac{60000}{2000000} = 0.03$$ --- 43. Problem 40: Probability of ball types. 44. Given: Baseballs 40%, Softballs 30%, Tennis balls 10%, Handballs remaining 20%. 45. (a) Baseball: $$P = 0.40$$ 46. (b) Tennis ball: $$P = 0.10$$ 47. (c) Not softball: $$P = 1 - 0.30 = 0.70$$ 48. (d) Handball: $$P = 0.20$$ --- 49. Problem 41: Lactose intolerance in African, Asian, Native Americans. 50. Given: 75% affected. 51. Probability lactose intolerant: $$P = 0.75$$ --- 52. Problem 42: Lactose intolerance in non-Hispanic white Americans. 53. Given: 20% affected. 54. Probability lactose intolerant: $$P = 0.20$$ --- 55. Problem 43: Probability transferred employee is a woman. 56. Given: 3 women out of 9 employees. 57. Probability woman transferred: $$P = \frac{3}{9} = \frac{1}{3} \approx 0.3333$$ --- 58. Problem 44: Probability tube is not defective. 59. Given: 6 defective out of 500. 60. Probability not defective: $$P = 1 - \frac{6}{500} = 1 - 0.012 = 0.988$$ --- 61. Problem 45: Probability professor grades completed project. 62. Given: 6 projects, student completed 2. 63. Probability: $$P = \frac{2}{6} = \frac{1}{3} \approx 0.3333$$ --- 64. Problem 46: Probability of penny in Meow Chow bag. 65. Given: 10,000 bags, 9922 pennies. 66. Probability penny: $$P = \frac{9922}{10000} = 0.9922$$ --- 67. Problem 47: Probability stopped driver is dark-skinned and not violating law. 68. Given: 22% drivers dark-skinned, 39% stopped drivers dark-skinned. 69. Probability stopped driver dark-skinned: $$P = 0.39$$ 70. Since 39% > 22%, NAACP claim that dark-skinned drivers stopped disproportionately seems reasonable. --- 71. Problem 55: Probability of guessing correct answer on first matching question. 72. Given: 8 possible matches. 73. Probability correct guess: $$P = \frac{1}{8} = 0.125$$ --- Final answers summarized for each problem.