投票箱抽取的频率与概率模拟
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该范例通过三维长方体(投票箱)和内部球体,动态演示从投票箱中抽取球体的频率与理论概率之间的关系。核心数学概念包括概率统计、频率与概率的对比、假设检验、指数函数以及三维向量与几何体。作图要点:使用GeoGebra的Polygon、Circle、Sequence、CountIf、Element、Point、Segment、Vector等命令构建三维投票箱和球体,并通过滑块(Speed)控制抽取次数,实时统计频率,同时用指数函数拟合或对比理论概率。适合高中及大学概率统计课程,用于直观理解大数定律和频率稳定于概率的现象,也可用于假设检验的演示。
GeoGebra 命令及参数
Polygon(E, F, 4) → poly1, e_1, f_1, h, i, G, HCircle(C, 1) → k_1Circle(A, 1) → pCircle(AA, 1) → tCircle(I, 1) → c_1Circle(M, 1) → d_1Circle(J, 1) → g_1Sequence(Random[1, 6], i, 1, 1000) → liste1First(liste1, n) → TirageCountIf(x ≟ 1, Tirage) → B3CountIf(x ≟ 2, Tirage) → B4CountIf(x ≟ 3, Tirage) → B5CountIf(x ≟ 4, Tirage) → B6CountIf(x ≟ 5, Tirage) → B7CountIf(x ≟ 6, Tirage) → B8Element(liste1, n) → ddCircle(O, 1) → eCircle(O, 1) → fCircle(O, 1) → gCircle(O, 1) → qCircle(O, 1) → rCircle(O, 1) → sPoint(h) → PPoint(h) → QSegment(P, Q) → jSegment(R, S) → mSegment(R, T) → a_1Point(m) → UPoint(m) → VPoint(m) → WPoint(m) → ZPoint(m) → A_1Point(m) → B_1Point(m) → C_1Point(m) → D_1Point(m) → E_1Point(m) → F_1Polygon(U, V, I_1, G_1) → poly2, u, v, i_1, g_2Polygon(W, J_1, K_1, Z) → poly3, w, j_1, k_2, zPolygon(A_1, B_1, M_1, L_1) → poly4, a_2, b_1, m_1, l_1Polygon(N_1, O_1, D_1, C_1) → poly5, n_1, o_1, d_2, c_2Point(m) → P_1Point(m) → Q_1Polygon(E_1, F_1, S_1, R_1) → poly6, e_2, f_2, s_1, r_1Polygon(P_1, Q_1, U_1, T_1) → poly7, p_1, q_1, u_1, t_1Point(a_1) → H_1Point(a_1) → V_1Point(a_1) → W_1Point(a_1) → Z_1Point(a_1) → A_2Point(a_1) → B_2Point(a_1) → C_2Vector(R, T) → v_1Polygon(P_1, D_2, F_2, Q_1) → poly8, p_2, d_3, f_3, q_2Polygon(H_2, G_2, F_1, E_1) → poly9, h_2, g_3, f_4, e_3Polygon(J_2, I_2, D_1, C_1) → poly10, j_2, i_2, d_4, c_3Polygon(L_2, K_2, B_1, A_1) → poly11, l_2, k_3, b_2, a_3Polygon(N_2, M_2, Z, W) → poly12, n_2, m_2, z_1, w_1Polygon(P_2, O_2, V, U) → poly13, p_3, o_2, v_2, u_2Circle(Q_2, 1) → h_1Circle(R_2, 1) → r_2Circle(S_2, 1) → s_2Circle(T_2, 1) → t_2Circle(U_2, 1) → h_3Circle(V_2, 1) → q_3
AI 绘图提示语参考
绘制一个三维长方体投票箱,内部放置六个彩色球体,分别代表六种抽取结果。箱体由多个多边形面构成,每个面用线段和点定位。在箱体前方或侧面,用圆形和线段构建动态统计图表,显示每次抽取后各结果的频数与理论概率的对比。添加一个滑块控制抽取次数,并让每次抽取的球体高亮显示。整体布局需清晰展示随机抽取过程、频数累积和概率收敛趋势,强调经验频率与理论概率的关系。
以上提示语为根据原始绘图命令整理而来,仅供参考。