Date: 5 6 月 2014

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第3次取完紅球

第4次取完紅球

第5次取完紅球

第6次取完紅球

第7次取完紅球

最後一球一定是綠球

可能的情況

1

2

3

4

5

6

7

8

\frac{8!}{5!×3!}

P(紅球先取完)=

=\frac{5}{8}

n = 0 (slider from 0 to 18, step 1)
r = 3 (slider from 3 to 9, step 1)
g = 5 (slider from 3 to 9, step 1)
text_Q: "一個不透明的袋中裝有大小相同的綠球" + (LaTeX[g]) + "個，\;紅球" + (LaTeX[r]) + "個，\;今袋中每次取一球，\;取後不放回，\;試求紅球先取完的機率."
A = (1.5704925480055298, 4.355533346146449)
listG = Sequence(Circle[A + (k, 0), 0.4], k, 1, g)
listR = Sequence(Circle[A + (k + g, 0), 0.4], k, 1, r)
k = 1.3
C: A - (0, (2 * k))
D: A - (0, (3 * k))
E: A - (0, (4 * k))
F: A - (0, (5 * k))
G: A - (0, (6 * k))
list1 = Sequence(Circle[C + (k, 0), 0.4], k, 1, r + g)
list2 = Sequence(Circle[D + (k, 0), 0.4], k, 1, r + g)
list3 = Sequence(Circle[E + (k, 0), 0.4], k, 1, r + g)
list4 = Sequence(Circle[F + (k, 0), 0.4], k, 1, r + g)
list5 = Sequence(Circle[G + (k, 0), 0.4], k, 1, r + g)
c_1 = Circle(C + (3, 0), 0.4)
c_2 = Circle(D + (4, 0), 0.4)
c_3 = Circle(E + (5, 0), 0.4)
c_4 = Circle(F + (6, 0), 0.4)
c_5 = Circle(G + (7, 0), 0.4)
list_{G1} = Sequence(Circle[C + (k, 0), 0.4], k, 4, r + g)
list_{G2} = Sequence(Circle[D + (k, 0), 0.4], k, 5, r + g)
list_{G3} = Sequence(Circle[E + (k, 0), 0.4], k, 6, r + g)
list_{G4} = Sequence(Circle[F + (k, 0), 0.4], k, 7, r + g)
list_{G5} = Sequence(Circle[G + (k, 0), 0.4], k, 8, r + g)
text0: "" + (LaTeX[g]) + "個綠球，\;" + (LaTeX[r]) + "個紅球"
p_1 = PolyLine(C + (7.5, 0.5), C + (8.5, 0.5), G + (8.5, (-0.5)), G + (7.5, (-0.5)), C + (7.5, 0.5))
B: A - (0, k)
list8 = Sequence(Circle[C + (k, 0), 0.4], k, 1, g + r)
A_1: A + (1, 0)
A_2: A + (2, 0)
A_3: A + (3, 0)
A_4: A + (4, 0)
A_5: A + (5, 0)
A_6: A + (6, 0)
A_7: A + (7, 0)
A_8: A + (8, 0)
C_1: C + (1, 0)
C_2: C + (2, 0)
C_3: C + (3, 0)
C_4: C + (4, 0)
C_5: C + (5, 0)
C_6: C + (6, 0)
C_7: C + (7, 0)
C_8: C + (8, 0)
t1 = 0 (slider from 0 to 1, step 0.001)
B_3: A_3 + (t1 * Vector[A_3, C_8])
t2 = 0 (slider from 0 to 1, step 0.001)
g_3 = Circle(B_3, 0.4)
B_1: A_1 + (t2 * Vector[A_1, C_3])
B_2: A_2 + (t2 * Vector[A_2, C_1])
B_4: A_4 + (t2 * Vector[A_4, C_6])
B_5: A_5 + (t2 * Vector[A_5, C_4])
B_6: A_6 + (t2 * Vector[A_6, C_2])
B_7: A_7 + (t2 * Vector[A_7, C_5])
B_8: A_8 + (t2 * Vector[A_8, C_7])
g_1 = Circle(B_1, 0.4)
g_2 = Circle(B_2, 0.4)
g_4 = Circle(B_4, 0.4)
g_5 = Circle(B_5, 0.4)
r_6 = Circle(B_6, 0.4)
r_7 = Circle(B_7, 0.4)
r_8 = Circle(B_8, 0.4)
text8: "1×" + (LaTeX[If[n ≥ 16, "\frac{7!}{4!×3!}"]]) + ""
a_0 = Segment(A + (2.7, (-5)), A + (5, (-5)))