幾何分配探討遊戲抽卡機率首次抽卡抽中機率-排列組合機率51

重複進行伯努利試驗，探討第一次出現某種結果，稱為幾何機率分布，探討第r次出現某種結果，稱為負二項機率分布。

常用計算於順序序列，取r=1，此負二項分布稱為Geom(P)幾何分布 = F(X=x) ～ NB(r,P)=NB(1,1-P)其函數f(k;1,P)=P (1-P)^k。K∈{1,2,3,...}，期望值=1/P，K∈{0,1,2,3,...}，期望值=1-P/P。

若隨機變量服從參數為P(X)的幾何分布，則記為 X ~ GE(P)。

 

假設抽到某張卡片的證真機率是5%(0.05)，X～GE(P=0.05)，當重複進行抽卡試驗，探討當第一次抽到某張卡片的證真機率為多少，這就是探討負二項機率分布的重複試驗中，首次出現某種結果的幾何分布機率問題。

 

推算如下，你想一次就抽中，須要95%的幸運值，你想一百次才抽中，須要0.59%的幸運值。14抽就抽中1次，在自己之前有51.23%的人，18抽就抽中1次，在自己之前有60.23%的人。

你知道嗎？你的抽卡運可能比你想像中的還要差喔！ 【譯人說統計】#1 幾何分配

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輸入證真機率	0.05
X次數	證真機率	證假機率	首次證真機率P(X) X [1-P(X)]^X-1	機率累積FX(N) FX(N)=1 －∞∑x=1  P(X) X [1-P(X)]^X-1= 1 。	備註	與所有人做比較值機率累積FX(N)=1 －∞∑x=1  P(X) X [1-P(X)]^X-1= 1 。
X	P(X)	1-P(X)	=B9*C9^(A9-1)	當多少次，包含自己的抽到機率是多少：在自己之前有多少百分比的人	表示比自己(不包含自己)少次數的機率總和的值是：	用100%扣除，表示自己的抽到的幸運值是：
1	0.05	0.95	5.00%	5.00%	0.00%	95.00%
2	0.05	0.95	4.75%	9.75%	5.00%	90.25%
3	0.05	0.95	4.51%	14.26%	9.75%	85.74%
4	0.05	0.95	4.29%	18.55%	14.26%	81.45%
5	0.05	0.95	4.07%	22.62%	18.55%	77.38%
6	0.05	0.95	3.87%	26.49%	22.62%	73.51%
7	0.05	0.95	3.68%	30.17%	26.49%	69.83%
8	0.05	0.95	3.49%	33.66%	30.17%	66.34%
9	0.05	0.95	3.32%	36.98%	33.66%	63.02%
10	0.05	0.95	3.15%	40.13%	36.98%	59.87%
11	0.05	0.95	2.99%	43.12%	40.13%	56.88%
12	0.05	0.95	2.84%	45.96%	43.12%	54.04%
13	0.05	0.95	2.70%	48.67%	45.96%	51.33%
14	0.05	0.95	2.57%	51.23%	48.67%	48.77%
15	0.05	0.95	2.44%	53.67%	51.23%	46.33%
16	0.05	0.95	2.32%	55.99%	53.67%	44.01%
17	0.05	0.95	2.20%	58.19%	55.99%	41.81%
18	0.05	0.95	2.09%	60.28%	58.19%	39.72%
19	0.05	0.95	1.99%	62.26%	60.28%	37.74%
20	0.05	0.95	1.89%	64.15%	62.26%	35.85%
21	0.05	0.95	1.79%	65.94%	64.15%	34.06%
22	0.05	0.95	1.70%	67.65%	65.94%	32.35%
23	0.05	0.95	1.62%	69.26%	67.65%	30.74%
24	0.05	0.95	1.54%	70.80%	69.26%	29.20%
25	0.05	0.95	1.46%	72.26%	70.80%	27.74%
26	0.05	0.95	1.39%	73.65%	72.26%	26.35%
27	0.05	0.95	1.32%	74.97%	73.65%	25.03%
28	0.05	0.95	1.25%	76.22%	74.97%	23.78%
29	0.05	0.95	1.19%	77.41%	76.22%	22.59%
30	0.05	0.95	1.13%	78.54%	77.41%	21.46%
31	0.05	0.95	1.07%	79.61%	78.54%	20.39%
32	0.05	0.95	1.02%	80.63%	79.61%	19.37%
33	0.05	0.95	0.97%	81.60%	80.63%	18.40%
34	0.05	0.95	0.92%	82.52%	81.60%	17.48%
35	0.05	0.95	0.87%	83.39%	82.52%	16.61%
36	0.05	0.95	0.83%	84.22%	83.39%	15.78%
37	0.05	0.95	0.79%	85.01%	84.22%	14.99%
38	0.05	0.95	0.75%	85.76%	85.01%	14.24%
39	0.05	0.95	0.71%	86.47%	85.76%	13.53%
40	0.05	0.95	0.68%	87.15%	86.47%	12.85%
41	0.05	0.95	0.64%	87.79%	87.15%	12.21%
42	0.05	0.95	0.61%	88.40%	87.79%	11.60%
43	0.05	0.95	0.58%	88.98%	88.40%	11.02%
44	0.05	0.95	0.55%	89.53%	88.98%	10.47%
45	0.05	0.95	0.52%	90.06%	89.53%	9.94%
46	0.05	0.95	0.50%	90.55%	90.06%	9.45%
47	0.05	0.95	0.47%	91.03%	90.55%	8.97%
48	0.05	0.95	0.45%	91.47%	91.03%	8.53%
49	0.05	0.95	0.43%	91.90%	91.47%	8.10%
50	0.05	0.95	0.40%	92.31%	91.90%	7.69%
51	0.05	0.95	0.38%	92.69%	92.31%	7.31%
52	0.05	0.95	0.37%	93.06%	92.69%	6.94%
53	0.05	0.95	0.35%	93.40%	93.06%	6.60%
54	0.05	0.95	0.33%	93.73%	93.40%	6.27%
55	0.05	0.95	0.31%	94.05%	93.73%	5.95%
56	0.05	0.95	0.30%	94.34%	94.05%	5.66%
57	0.05	0.95	0.28%	94.63%	94.34%	5.37%
58	0.05	0.95	0.27%	94.90%	94.63%	5.10%
59	0.05	0.95	0.26%	95.15%	94.90%	4.85%
60	0.05	0.95	0.24%	95.39%	95.15%	4.61%
61	0.05	0.95	0.23%	95.62%	95.39%	4.38%
62	0.05	0.95	0.22%	95.84%	95.62%	4.16%
63	0.05	0.95	0.21%	96.05%	95.84%	3.95%
64	0.05	0.95	0.20%	96.25%	96.05%	3.75%
65	0.05	0.95	0.19%	96.44%	96.25%	3.56%
66	0.05	0.95	0.18%	96.61%	96.44%	3.39%
67	0.05	0.95	0.17%	96.78%	96.61%	3.22%
68	0.05	0.95	0.16%	96.94%	96.78%	3.06%
69	0.05	0.95	0.15%	97.10%	96.94%	2.90%
70	0.05	0.95	0.15%	97.24%	97.10%	2.76%
71	0.05	0.95	0.14%	97.38%	97.24%	2.62%
72	0.05	0.95	0.13%	97.51%	97.38%	2.49%
73	0.05	0.95	0.12%	97.64%	97.51%	2.36%
74	0.05	0.95	0.12%	97.75%	97.64%	2.25%
75	0.05	0.95	0.11%	97.87%	97.75%	2.13%
76	0.05	0.95	0.11%	97.97%	97.87%	2.03%
77	0.05	0.95	0.10%	98.07%	97.97%	1.93%
78	0.05	0.95	0.10%	98.17%	98.07%	1.83%
79	0.05	0.95	0.09%	98.26%	98.17%	1.74%
80	0.05	0.95	0.09%	98.35%	98.26%	1.65%
81	0.05	0.95	0.08%	98.43%	98.35%	1.57%
82	0.05	0.95	0.08%	98.51%	98.43%	1.49%
83	0.05	0.95	0.07%	98.58%	98.51%	1.42%
84	0.05	0.95	0.07%	98.65%	98.58%	1.35%
85	0.05	0.95	0.07%	98.72%	98.65%	1.28%
86	0.05	0.95	0.06%	98.79%	98.72%	1.21%
87	0.05	0.95	0.06%	98.85%	98.79%	1.15%
88	0.05	0.95	0.06%	98.90%	98.85%	1.10%
89	0.05	0.95	0.05%	98.96%	98.90%	1.04%
90	0.05	0.95	0.05%	99.01%	98.96%	0.99%
91	0.05	0.95	0.05%	99.06%	99.01%	0.94%
92	0.05	0.95	0.05%	99.11%	99.06%	0.89%
93	0.05	0.95	0.04%	99.15%	99.11%	0.85%
94	0.05	0.95	0.04%	99.19%	99.15%	0.81%
95	0.05	0.95	0.04%	99.23%	99.19%	0.77%
96	0.05	0.95	0.04%	99.27%	99.23%	0.73%
97	0.05	0.95	0.04%	99.31%	99.27%	0.69%
98	0.05	0.95	0.03%	99.34%	99.31%	0.66%
99	0.05	0.95	0.03%	99.38%	99.34%	0.62%
100	0.05	0.95	0.03%	99.41%	99.38%	0.59%