2024 年 5 月 15 日至 17 日“一书一赛”水上运动大赛在重庆彭水举行, 甲、乙、丙、丁、戊 5名志愿者承担调度服务、安检服务、驾驶服务 3个项目志愿服务, 每项工作至少需要1名志愿者, 甲不承担驾驶服务, 则不同的安排方法有 _____ 种.(用数字作答)---**Question 19:** Text: 袋中装有 5 张相同的卡片, 分别标有数字 1, 2, 3, 4, 5, 从中有放回地随机取两次, 每次取 1 张卡片, A表示事件“第一次取出的卡片数字是奇数”, B表示事件“第二次取出的卡片数字是偶数”, C表示事件“两次取出的卡片数字之和是 6”, 则 A. P(A∪B) = 1 B. P(B∪C) = 13/25 C. A与B相互独立 D. P(C|B) = 1/5 Other Relevant Text/Calculations: P(C|B) = 1/5 circled. A and D circled. **Question 22:** Text: 下列说法正确的是 A. 若A, B两组组成对数据的样本相关系数分别为 r_A = 0.97, r_B = -0.99, 则B组数据比A组数据的相关性更强 B. 若y关于x的经验回归方程为 ŷ = -0.6x + 0.2, 则样本点(1, -2)的残差为 -2.4 C. 已知随机变量X服从二项分布 B(n, 1/4), 若 E(3X + 1) = 7, 则 n = 8 D. 已知随机变量 ξ ~ N(2, 81), 若 ξ = 3η + 1, 则 D(η) = 9 Other Relevant Text/Calculations: A, C, D circled. A and D marked with a check/tick. Calculation notes: E(ax+b) = aE(x)+b D(ax+b) = a^2 D(x) For C: E(3X+1) = 3E(X)+1 = 7 => 3E(X)=6 => E(X)=2. For B(n,p), E(X)=np. 2 = n * 1/4 => n=8. For D: ξ ~ N(2, 81). E(ξ) = 2, D(ξ) = 81. ξ = 3η + 1. D(ξ) = D(3η+1) = 3^2 D(η) = 9 D(η). 81 = 9 D(η) => D(η) = 9. **Question 25:** Text: 2024 年 5 月 15 日至 17 日“一书一赛”水上运动大赛在重庆彭水举行, 甲、乙、丙、丁、戊 5名志愿者承担调度服务、安检服务、驾驶服务 3个项目志愿服务, 每项工作至少需要1名志愿者, 甲不承担驾驶服务, 则不同的安排方法有 _____ 种.(用数字作答) Other Relevant Text/Calculations: Handwritten note near blank: 180. Handwritten combinatorics notation: C(4,?) A(5,?) A(3,?). **Question 26:** Text: 若 (x - 2)^4 = a_4 x^4 + a_3 x^3 + a_2 x^2 + a_1 x + a_0, 则 a_0 = ____ ; a_1 + a_3 / a_0 + a_2 + a_4 = ____ . Other Relevant Text/Calculations: Handwritten note near first blank: 16. Binomial expansion note: C(4,k) x^k (-2)^(4-k) Calculations for coefficients: k=0: C(4,0) * (-2)^4 = 1 * 16 = 16 = a0 k=1: C(4,1) * (-2)^3 = 4 * (-8) = -32 = a1 k=2: C(4,2) * (-2)^2 = 6 * 4 = 24 = a2 k=3: C(4,3) * (-2)^1 = 4 * (-2) = -8 = a3 k=4: C(4,4) * (-2)^0 = 1 * 1 = 1 = a4 Calculation for the second expression: (a1 + a3) / (a0 + a2 + a4) = (-32 + -8) / (16 + 24 + 1) = -40 / 41. Handwritten note near second blank: -40/41.