क्रेप्स में रोल की संख्या तालिका

परिचय

मुझसे अक्सर एक सवाल पूछा जाता है, "क्रेप्स में किसी शूटर के x रोल तक टिके रहने की प्रायिकता क्या है?" नीचे दी गई तालिका 50 रोल तक के लिए इस सवाल का जवाब देती है। पहला कॉलम रोल नंबर है। दूसरा कॉलम ठीक उसी रोल पर सात आउट होने की प्रायिकता है। तीसरा कॉलम उस रोल के बाद बचे रहने की प्रायिकता है।

1 से 50 रोल के लिए क्रेप्स सर्वाइवल टेबल

रोल संख्या	संभावना सेवन-आउट	संभावना उत्तरजीविता
1	0.00000000	1.00000000
2	0.11111111	0.88888889
3	0.11676955	0.77211934
4	0.10476680	0.66735254
5	0.09122363	0.57612891
6	0.07891804	0.49721087
7	0.06816676	0.42904411
8	0.05885276	0.37019135
9	0.05080065	0.31939070
10	0.04384414	0.27554656
11	0.03783614	0.23771043
12	0.03264850	0.20506193
13	0.02817002	0.17689190
14	0.02430433	0.15258757
15	0.02096801	0.13161956
16	0.01808886	0.11353070
17	0.01560445	0.09792625
18	0.01346084	0.08446541
19	0.01161138	0.07285403
20	0.01001580	0.06283823
21	0.00863931	0.05419892
22	0.00745187	0.04674705
23	0.00642755	0.04031950
24	0.00554396	0.03477554
25	0.00478180	0.02999374
26	0.00412437	0.02586937
27	0.00355731	0.02231206
28	0.00306819	0.01924387
29	0.00264632	0.01659755
30	0.00228244	0.01431511
31	0.00196858	0.01234653
32	0.00169788	0.01064864
33	0.00146440	0.00918424
34	0.00126303	0.00792121
35	0.00108934	0.00683187
36	0.00093954	0.00589234
37	0.00081033	0.00508201
38	0.00069890	0.00438311
39	0.00060278	0.00378033
40	0.00051989	0.00326044
41	0.00044839	0.00281205
42	0.00038673	0.00242532
43	0.00033354	0.00209178
44	0.00028767	0.00180411
45	0.00024811	0.00155600
46	0.00021399	0.00134201
47	0.00018456	0.00115745
48	0.00015918	0.00099827
49	0.00013729	0.00086098
50	0.00011841	0.00074257

अगली तालिका में भी यही जानकारी दी गई है, लेकिन 200 रोल तक के लिए। संभावनाएँ बहुत कम हो जाती हैं, इसलिए यह तालिका वैज्ञानिक संकेतन में है।

1 से 200 रोल के लिए क्रेप्स सर्वाइवल टेबल

रोल संख्या	संभावना सेवन-आउट	संभावना उत्तरजीविता
1	0.000000ई+00	1.000000ई+00
2	1.111111ई-01	8.888889ई-01
3	1.167695ई-01	7.721193ई-01
4	1.047668ई-01	6.673525ई-01
5	9.122363ई-02	5.761289ई-01
6	7.891804ई-02	4.972109ई-01
7	6.816676ई-02	4.290441ई-01
8	5.885276ई-02	3.701913ई-01
9	5.080065ई-02	3.193907ई-01
10	4.384414ई-02	2.755466ई-01
11	3.783614ई-02	2.377104ई-01
12	3.264850ई-02	2.050619ई-01
13	2.817002ई-02	1.768919ई-01
14	2.430433ई-02	1.525876ई-01
15	2.096801ई-02	1.316196ई-01
16	1.808886ई-02	1.135307ई-01
17	1.560445ई-02	9.792625ई-02
18	1.346084ई-02	8.446541ई-02
19	1.161138ई-02	7.285403ई-02
20	1.001580ई-02	6.283823ई-02
21	8.639309ई-03	5.419892ई-02
22	7.451869ई-03	4.674705ई-02
23	6.427548ई-03	4.031950ई-02
24	5.543963ई-03	3.477554ई-02
25	4.781795ई-03	2.999374ई-02
26	4.124373ई-03	2.586937ई-02
27	3.557310ई-03	2.231206ई-02
28	3.068195ई-03	1.924387ई-02
29	2.646317ई-03	1.659755ई-02
30	2.282437ई-03	1.431511ई-02
31	1.968585ई-03	1.234653ई-02
32	1.697884ई-03	1.064864ई-02
33	1.464404ई-03	9.184241ई-03
34	1.263027ई-03	7.921214ई-03
35	1.089340ई-03	6.831874ई-03
36	9.395362ई-04	5.892338ई-03
37	8.103321ई-04	5.082006ई-03
38	6.988952ई-04	4.383111ई-03
39	6.027824ई-04	3.780328ई-03
40	5.198867ई-04	3.260442ई-03
41	4.483907ई-04	2.812051ई-03
42	3.867267ई-04	2.425324ई-03
43	3.335427ई-04	2.091782ई-03
44	2.876726ई-04	1.804109ई-03
45	2.481107ई-04	1.555998ई-03
46	2.139894ई-04	1.342009ई-03
47	1.845605ई-04	1.157448ई-03
48	1.591789ई-04	9.982695ई-04
49	1.372878ई-04	8.609818ई-04
50	1.184072ई-04	7.425745ई-04
51	1.021232ई-04	6.404513ई-04
52	8.807867ई-05	5.523726ई-04
53	7.596559ई-05	4.764071ई-04
54	6.551837ई-05	4.108887ई-04
55	5.650790ई-05	3.543808ई-04
56	4.873660ई-05	3.056442ई-04
57	4.203405ई-05	2.636101ई-04
58	3.625328ई-05	2.273569ई-04
59	3.126751ई-05	1.960893ई-04
60	2.696741ई-05	1.691219ई-04
61	2.325869ई-05	1.458632ई-04
62	2.006001ई-05	1.258032ई-04
63	1.730124ई-05	1.085020ई-04
64	1.492187ई-05	9.358012ई-05
65	1.286972ई-05	8.071040ई-05
66	1.109980ई-05	6.961061ई-05
67	9.573283ई-06	6.003732ई-05
68	8.256706ई-06	5.178062ई-05
69	7.121193ई-06	4.465942ई-05
70	6.141842ई-06	3.851758ई-05
71	5.297178ई-06	3.322040ई-05
72	4.568677ई-06	2.865173ई-05
73	3.940364ई-06	2.471136ई-05
74	3.398461ई-06	2.131290ई-05
75	2.931083ई-06	1.838182ई-05
76	2.527982ई-06	1.585384ई-05
77	2.180319ई-06	1.367352ई-05
78	1.880468ई-06	1.179305ई-05
79	1.621854ई-06	1.017120ई-05
80	1.398806ई-06	8.772390ई-06
81	1.206434ई-06	7.565956ई-06
82	1.040518ई-06	6.525439ई-06
83	8.974191ई-07	5.628020ई-06
84	7.740004ई-07	4.854019ई-06
85	6.675550ई-07	4.186464ई-06
86	5.757487ई-07	3.610715ई-06
87	4.965681ई-07	3.114147ई-06
88	4.282770ई-07	2.685870ई-06
89	3.693777ई-07	2.316493ई-06
90	3.185785ई-07	1.997914ई-06
91	2.747656ई-07	1.723148ई-06
92	2.369781ई-07	1.486170ई-06
93	2.043874ई-07	1.281783ई-06
94	1.762788ई-07	1.105504ई-06
95	1.520358ई-07	9.534683ई-07
96	1.311269ई-07	8.223414ई-07
97	1.130935ई-07	7.092478ई-07
98	9.754019ई-08	6.117076ई-07
99	8.412586ई-08	5.275818ई-07
100	7.255634ई-08	4.550254ई-07
101	6.257794ई-08	3.924475ई-07
102	5.397183ई-08	3.384757ई-07
103	4.654929ई-08	2.919264ई-07
104	4.014754ई-08	2.517788ई-07
105	3.462620ई-08	2.171526ई-07
106	2.986419ई-08	1.872885ई-07
107	2.575708ई-08	1.615314ई-07
108	2.221480ई-08	1.393166ई-07
109	1.915969ई-08	1.201569ई-07
110	1.652473ई-08	1.036322ई-07
111	1.425214ई-08	8.938002ई-08
112	1.229210ई-08	7.708792ई-08
113	1.060161ई-08	6.648631ई-08
114	9.143612ई-09	5.734269ई-08
115	7.886126ई-09	4.945657ई-08
116	6.801576ई-09	4.265499ई-08
117	5.866181ई-09	3.678881ई-08
118	5.059427ई-09	3.172938ई-08
119	4.363623ई-09	2.736576ई-08
120	3.763510ई-09	2.360225ई-08
121	3.245929ई-09	2.035632ई-08
122	2.799529ई-09	1.755679ई-08
123	2.414520ई-09	1.514227ई-08
124	2.082460ई-09	1.305981ई-08
125	1.796067ई-09	1.126375ई-08
126	1.549061ई-09	9.714685ई-09
127	1.336024ई-09	8.378661ई-09
128	1.152286ई-09	7.226375ई-09
129	9.938163ई-10	6.232559ई-09
130	8.571405ई-10	5.375419ई-09
131	7.392611ई-10	4.636157ई-09
132	6.375933ई-10	3.998564ई-09
133	5.499075ई-10	3.448657ई-09
134	4.742808ई-10	2.974376ई-09
135	4.090547ई-10	2.565321ई-09
136	3.527990ई-10	2.212522ई-09
137	3.042799ई-10	1.908242ई-09
138	2.624334ई-10	1.645809ई-09
139	2.263419ई-10	1.419467ई-09
140	1.952140ई-10	1.224253ई-09
141	1.683669ई-10	1.055886ई-09
142	1.452120ई-10	9.106740ई-10
143	1.252416ई-10	7.854324ई-10
144	1.080176ई-10	6.774148ई-10
145	9.316232ई-11	5.842525ई-10
146	8.035006ई-11	5.039024ई-10
147	6.929981ई-11	4.346026ई-10
148	5.976927ई-11	3.748334ई-10
149	5.154943ई-11	3.232839ई-10
150	4.446003ई-11	2.788239ई-10
151	3.834561ई-11	2.404783ई-10
152	3.307208ई-11	2.074062ई-10
153	2.852380ई-11	1.788824ई-10
154	2.460103ई-11	1.542814ई-10
155	2.121774ई-11	1.330637ई-10
156	1.829975ई-11	1.147639ई-10
157	1.578305ई-11	9.898086ई-11
158	1.361247ई-11	8.536839ई-11
159	1.174039ई-11	7.362800ई-11
160	1.012578ई-11	6.350222ई-11
161	8.733222ई-12	5.476899ई-11
162	7.532174ई-12	4.723682ई-11
163	6.496303ई-12	4.074052ई-11
164	5.602891ई-12	3.513763ई-11
165	4.832346ई-12	3.030528ई-11
166	4.167772ई-12	2.613751ई-11
167	3.594594ई-12	2.254292ई-11
168	3.100243ई-12	1.944267ई-11
169	2.673878ई-12	1.676880ई-11
170	2.306150ई-12	1.446265ई-11
171	1.988993ई-12	1.247365ई-11
172	1.715455ई-12	1.075820ई-11
173	1.479535ई-12	9.278663ई-12
174	1.276060ई-12	8.002603ई-12
175	1.100568ई-12	6.902035ई-12
176	9.492110ई-13	5.952824ई-12
177	8.186696ई-13	5.134155ई-12
178	7.060810ई-13	4.428074ई-12
179	6.089764ई-13	3.819097ई-12
180	5.252261ई-13	3.293871ई-12
181	4.529938ई-13	2.840877ई-12
182	3.906952ई-13	2.450182ई-12
183	3.369644ई-13	2.113218ई-12
184	2.906229ई-13	1.822595ई-12
185	2.506546ई-13	1.571940ई-12
186	2.161831ई-13	1.355757ई-12
187	1.864522ई-13	1.169305ई-12
188	1.608101ई-13	1.008495ई-12
189	1.386945ई-13	8.698004ई-13
190	1.196204ई-13	7.501800ई-13
191	1.031694ई-13	6.470106ई-13
192	8.898094ई-14	5.580296ई-13
193	7.674372ई-14	4.812859ई-13
194	6.618945ई-14	4.150965ई-13
195	5.708666ई-14	3.580098ई-13
196	4.923575ई-14	3.087741ई-13
197	4.246454ई-14	2.663095ई-13
198	3.662455ई-14	2.296850ई-13
199	3.158771ई-14	1.980973ई-13
200	2.724357ई-14	1.708537ई-13

प्रति शूटर रोल की औसत संख्या 8.525510 है।

मैंने इस समस्या को कैसे हल किया, इसके लिए कृपया मेरी MathProblems.info साइट, समस्या 204 देखें।

द्वारा लिखित: Michael Shackleford