Математика и информатика. Решение логико-познавательных задач. Учебное пособие для студентов вузов
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ɉɪɢ ɪɟɲɟɧɢɢ ɡɚɞɚɱ ɬɟɨɪɟɦɵ ɫɥɨɠɟɧɢɹ ɢ ɭɦɧɨɠɟɧɢɹ ɜɟɪɨɹɬɧɨɫɬɟɣ ɱɚɫɬɨ ɩɪɢɦɟɧɹɸɬɫɹ ɜɦɟɫɬɟ.
ɉɪɢɦɟɪ 57. Ɍɪɢ ɫɬɭɞɟɧɬɚ ɫɞɚɸɬ ɷɤɡɚɦɟɧ. ȼɟɪɨɹɬɧɨɫɬɶ ɫɞɚɬɶ ɷɤɡɚɦɟɧ ɧɚ «ɨɬɥɢɱɧɨ» ɞɥɹ ɩɟɪɜɨɝɨ, ɜɬɨɪɨɝɨ ɢ ɬɪɟɬɶɟɝɨ ɫɬɭɞɟɧɬɨɜ ɪɚɜɧɚ 0,7, 0,6 ɢ 0,2 ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ. Ʉɚɤɨɜɚ ɜɟɪɨɹɬɧɨɫɬɶ ɬɨɝɨ, ɱɬɨ ɷɤɡɚɦɟɧ ɛɭɞɟɬ ɫɞɚɧ ɧɚ «ɨɬɥɢɱɧɨ»: 1) ɬɨɥɶɤɨ ɨɞɧɢɦ ɫɬɭɞɟɧɬɨɦ (ɫɨɛɵɬɢɟ ȼ); 2) ɬɪɟɦɹ ɫɬɭɞɟɧɬɚɦɢ (ɫɨɛɵɬɢɟ ɋ); 3) ɧɢ ɨɞɧɢɦ ɢɡ ɫɬɭɞɟɧɬɨɜ (ɫɨɛɵɬɢɟ D); 4) ɬɨɥɶɤɨ ɞɜɭɦɹ ɫɬɭɞɟɧɬɚɦɢ (ɫɨɛɵɬɢɟ E); 5) ɬɨɥɶɤɨ ɬɪɟɬɶɢɦ ɫɬɭɞɟɧɬɨɦ (ɫɨɛɵɬɢɟ F)?
ȼɜɟɞɟɦ ɫɥɟɞɭɸɳɢɟ ɨɛɨɡɧɚɱɟɧɢɹ:
A1 — 1-ɣ ɫɬɭɞɟɧɬ ɫɞɚɫɬ ɷɤɡɚɦɟɧ ɧɚ ɨɬɥɢɱɧɨ, A1 — 1-ɵɣ ɫɬɭɞɟɧɬ
ɧɟ ɫɞɚɫɬ ɷɤɡɚɦɟɧ ɧɚ ɨɬɥɢɱɧɨ, P(A1) 0,7 , P(A1) 1 0,7 0,3 ;
A2 — 2-ɣ ɫɬɭɞɟɧɬ ɫɞɚɫɬ ɷɤɡɚɦɟɧ ɧɚ ɨɬɥɢɱɧɨ, A2 — 2-ɨɣ ɫɬɭɞɟɧɬ
ɧɟ ɫɞɚɫɬ ɷɤɡɚɦɟɧ ɧɚ ɨɬɥɢɱɧɨ, P(A2) 0,6 , P(A2 ) 1 0,6 0, 4 ;
A3 — 3-ɣ ɫɬɭɞɟɧɬ ɫɞɚɫɬ ɷɤɡɚɦɟɧ ɧɚ ɨɬɥɢɱɧɨ, A3 — 3-ɢɣ ɫɬɭɞɟɧɬ
ɧɟ ɫɞɚɫɬ ɷɤɡɚɦɟɧ ɧɚ ɨɬɥɢɱɧɨ, P(A1) 0, 2 , P(A1) 1 0, 2 0,8 . ɋɨɛɵɬɢɹ A1 , A2 , A3 — ɫɨɜɦɟɫɬɧɵ ɢ ɧɟɡɚɜɢɫɢɦɵ. ɉɪɢɦɟɧɹɹ ɬɟɨɪɟ-
ɦɵɫɥɨɠɟɧɢɹɢ ɭɦɧɨɠɟɧɢɹ, ɧɚɯɨɞɢɦɜɟɪɨɹɬɧɨɫɬɢɫɨɛɵɬɢɣB, C, D, E, F: 1) ɫɨɛɵɬɢɟ ȼ — ɷɤɡɚɦɟɧ ɛɭɞɟɬ ɫɞɚɧ ɧɚ «ɨɬɥɢɱɧɨ» ɬɨɥɶɤɨ ɨɞɧɢɦ
ɫɬɭɞɟɧɬɨɦ (ɪɢɫ. 4.7):
:
Ⱥ1 Ⱥ2
Ⱥ3
ǸȐș. 4.7
P(B) P(A1) P(A2 ) P(A3 ) P(A1) P(A2) P(A3 ) P(A1) P( A2 ) P( A3 )
P(B) 0,7 0, 4 0,8 0,3 0,6 0,8 0,3 0, 4 0, 2 0,392 ;
2) ɫɨɛɵɬɢɟ C — ɷɤɡɚɦɟɧ ɛɭɞɟɬ ɫɞɚɧ ɧɚ «ɨɬɥɢɱɧɨ» ɬɪɟɦɹ ɫɬɭɞɟɧɬɚ-
ɦɢ (ɪɢɫ. 4.8):
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:
Ⱥ1 Ⱥ2
Ⱥ3
ǸȐș. 4.8
P(C) P(A1) P(A2) P(A3 ) 0,7 0,6 0, 2 0,084 ;
3) ɫɨɛɵɬɢɟ D — ɧɢ ɨɞɢɧ ɢɡ ɫɬɭɞɟɧɬɨɜ ɧɟ ɫɞɚɫɬ ɷɤɡɚɦɟɧ ɧɚ «ɨɬɥɢɱ-
ɧɨ» (ɪɢɫ. 4.9):
:
Ⱥ1 Ⱥ2
Ⱥ3
ǸȐș. 4.9
P(D) P(A1) P(A2 ) P(A3 ) 0,3 0, 4 0,8 0,096 ;
4) ɫɨɛɵɬɢɟ E — ɷɤɡɚɦɟɧ ɛɭɞɟɬ ɫɞɚɧ ɧɚ «ɨɬɥɢɱɧɨ» ɬɨɥɶɤɨ ɞɜɭɦɹ ɫɬɭɞɟɧɬɚɦɢ (ɪɢɫ. 4.10):
:
Ⱥ1 Ⱥ2
Ⱥ3
ǸȐș. 4.10
102
P(E) P(A1) P(A2 ) P(A3 ) P(A1) P(A2) P(A3 ) P( A1) P( A2 ) P( A3 )
P(E) 0,7 0,6 0,8 0,3 0,6 0, 2 0,7 0, 4 0, 2 0, 428 ;
5) ɫɨɛɵɬɢɟ F — ɷɤɡɚɦɟɧ ɛɭɞɟɬ ɫɞɚɧ ɧɚ «ɨɬɥɢɱɧɨ» ɬɨɥɶɤɨ ɬɪɟɬɶɢɦ ɫɬɭɞɟɧɬɨɦ (ɪɢɫ. 4.11):
:
Ⱥ1 Ⱥ2
Ⱥ3
ǸȐș. 4.11
P(F) P(A1) P(A2 ) P(A3 ) 0,3 0, 4 0, 2 0,024 .
4.5. ǼȖȘȔțȓȈ ȗȖȓȕȖȑ ȊȍȘȖȧȚȕȖșȚȐ. ǼȖȘȔțȓȈ ǩȈȑȍșȈ
ɉɭɫɬɶ ɧɟɤɨɬɨɪɨɟ ɫɨɛɵɬɢɟ Ⱥ ɦɨɠɟɬ ɩɪɨɢɡɨɣɬɢ ɩɪɢ ɧɚɫɬɭɩɥɟɧɢɢ ɨɞɧɨɝɨ ɢ ɬɨɥɶɤɨ ɨɞɧɨɝɨ ɢɡ ɫɨɛɵɬɢɣ H1 , H2 ,..., Hn , ɧɚɡɵɜɚɟɦɵɯ ɝɢɩɨ-
ɬɟɡɚɦɢ ɢ ɨɛɪɚɡɭɸɳɢɯ ɩɨɥɧɭɸ ɝɪɭɩɩɭ ɧɟɫɨɜɦɟɫɬɧɵɯ ɫɨɛɵɬɢɣ.
Ɍɨɝɞɚ ɜɟɪɨɹɬɧɨɫɬɶ ɫɨɛɵɬɢɹ Ⱥ ɨɩɪɟɞɟɥɹɟɬɫɹ ɩɨ ɮɨɪɦɭɥɟ ɩɨɥɧɨɣ ɜɟ-
ɪɨɹɬɧɨɫɬɢ:
P(A) |
P(H1) P(A / H1) P(H2 ) P(A / H2 ) ... P(Hn ) P(A / Hn ) , |
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ɢɥɢ: |
P(A) ¦P(Hi ) P(A / Hi ) , |
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ɝɞɟ P(Hi ) — ɜɟɪɨɹɬɧɨɫɬɢ ɝɢɩɨɬɟɡ,
P(A / Hi ) — ɭɫɥɨɜɧɵɟ ɜɟɪɨɹɬɧɨɫɬɢ ɧɚɫɬɭɩɥɟɧɢɹ ɫɨɛɵɬɢɹ A ɫ ɤɚɠɞɨɣ
ɢɡ ɝɢɩɨɬɟɡ,
i 1, 2,...n — ɢɧɞɟɤɫ, ɨɛɨɡɧɚɱɚɸɳɢɣɧɨɦɟɪɫɨɨɬɜɟɬɫɬɜɭɸɳɟɣɝɢɩɨɬɟɡɵ.
Ɂɚɦɟɱɚɧɢɟ 3. ɑɢɫɥɨ ɫɥɚɝɚɟɦɵɯ ɜ ɮɨɪɦɭɥɟ ɩɨɥɧɨɣ ɜɟɪɨɹɬɧɨɫɬɢ ɜɫɟɝɞɚ ɪɚɜɧɨ ɤɨɥɢɱɟɫɬɜɭ ɝɢɩɨɬɟɡ, ɜɵɞɜɢɧɭɬɵɯ ɩɨ ɭɫɥɨɜɢɸ ɡɚɞɚɱɢ.
ɉɪɢɦɟɪ 58. ɂɡ ɩɭɧɤɬɚ Ɉ ɜɟɞɭɬ ɱɟɬɵɪɟ ɞɨɪɨɝɢ, ɩɪɨɯɨɞɹɳɢɟ ɱɟɪɟɡ ɩɭɧɤɬɵ H1 , H2 , H3 , H4 ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ (ɪɢɫ. 4.12). Ʉɚɤɨɜɚ ɜɟɪɨɹɬɧɨɫɬɶ
103
ɬɨɝɨ, ɱɬɨ ɩɭɬɧɢɤ, ɜɵɲɟɞɲɢɣ ɢɡ ɩɭɧɤɬɚ Ɉ, ɩɨɩɚɞɟɬ ɜ ɩɭɧɤɬ Ⱥ, ɟɫɥɢ ɨɧ ɩɨɣɞɟɬ ɩɨ ɧɚɭɝɚɞ ɜɵɛɪɚɧɧɨɣ ɞɨɪɨɝɟ?
ɋɨɛɵɬɢɟ Ⱥ — ɩɭɬɧɢɤ ɞɨɛɟɪɟɬɫɹ ɢɡ ɩɭɧɤɬɚ Ɉ ɜ ɩɭɧɤɬ Ⱥ ɩɨ ɧɚɭɝɚɞ ɜɵɛɪɚɧɧɨɣ ɞɨɪɨɝɟ.
Ƚɢɩɨɬɟɡɵ H1 , H2 , H3 , H4 — ɜɵɛɨɪ ɩɭɬɧɢɤɨɦ ɨɞɧɨɣ ɢɡ ɱɟɬɵɪɟɯ ɞɨɪɨɝ, ɩɪɨɯɨɞɹɳɢɯ ɱɟɪɟɡ ɩɭɧɤɬɵ H1 , H2 , H3 , H4 ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ.
Ɉɱɟɜɢɞɧɨ, ɱɬɨ ɞɚɧɧɵɟ ɝɢɩɨɬɟɡɵ ɪɚɜɧɨɜɟɪɨɹɬɧɵ (ɩɭɬɧɢɤ ɫ ɪɚɜɧɨɣ ɜɟɪɨɹɬɧɨɫɬɶɸ ɦɨɠɟɬ ɜɵɛɪɚɬɶ ɨɞɧɭ ɢɡ ɱɟɬɵɪɟɯ ɞɨɪɨɝ) ɢ ɨɛɪɚɡɭɸɬ ɩɨɥɧɭɸ ɝɪɭɩɩɭ ɧɟɫɨɜɦɟɫɬɧɵɯ ɫɨɛɵɬɢɣ:
P(H1) P(H2 ) P(H3 ) P(H4 ) |
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0, 25 . |
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ɋɞɟɥɚɟɦ ɩɪɨɜɟɪɤɭ (ɫɭɦɦɚ ɜɟɪɨɹɬɧɨɫɬɟɣ ɧɟɫɨɜɦɟɫɬɧɵɯ ɫɨɛɵɬɢɣ, ɨɛɪɚɡɭɸɳɢɯ ɩɨɥɧɭɸ ɝɪɭɩɩɭ, ɟɫɬɶ ɫɨɛɵɬɢɟ ɞɨɫɬɨɜɟɪɧɨɟ):
P(H1) P(H2 ) P(H3 ) P(H4 ) 0, 25 0, 25 0, 25 0, 25 1.
ɉɨ ɫɯɟɦɟ ɞɨɪɨɝ (ɫɦ. ɪɢɫ. 4.12) ɧɚɯɨɞɢɦ ɭɫɥɨɜɧɵɟ ɜɟɪɨɹɬɧɨɫɬɢ ɩɨɩɚɞɚɧɢɹ ɩɭɬɧɢɤɚ ɜ ɩɭɧɤɬ Ⱥ:
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H2 |
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Ɉ |
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Ⱥ |
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H3 |
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ǸȐș. 4.12 |
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P(A / H1) |
0 — ɜɟɪɨɹɬɧɨɫɬɶ ɩɨɩɚɫɬɶ ɜ ɩɭɧɤɬ Ⱥ, ɟɫɥɢ ɩɭɬɧɢɤ ɜɵɛɢ- |
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ɪɚɟɬ ɧɚɩɪɚɜɥɟɧɢɟ H1 ; |
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0,5 |
— ɜɟɪɨɹɬɧɨɫɬɶ ɩɨɩɚɫɬɶ ɜ ɩɭɧɤɬ Ⱥ, ɟɫɥɢ ɩɭɬɧɢɤ |
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ɜɵɛɢɪɚɟɬ ɧɚɩɪɚɜɥɟɧɢɟ H2 ; |
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P(A / H3 ) |
1 — ɜɟɪɨɹɬɧɨɫɬɶ ɩɨɩɚɫɬɶ ɜ ɩɭɧɤɬ Ⱥ, ɟɫɥɢ ɩɭɬɧɢɤ ɜɵɛɢ- |
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ɪɚɟɬ ɧɚɩɪɚɜɥɟɧɢɟ H3 ; |
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P(A / H4 ) |
0,5 — ɜɟɪɨɹɬɧɨɫɬɶ ɩɨɩɚɫɬɶ ɜ ɩɭɧɤɬ Ⱥ, ɟɫɥɢ ɩɭɬɧɢɤ ɜɵ- |
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ɛɢɪɚɟɬ ɧɚɩɪɚɜɥɟɧɢɟ H4 . |
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ɇɚɣɞɟɧɧɵɟ ɜɟɪɨɹɬɧɨɫɬɢ ɭɞɨɛɧɨ ɡɚɩɢɫɚɬɶ ɜ ɬɚɛɥ. 4.1. |
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ǺȈȉȓȐȞȈ 4.1 |
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P(Hi ) |
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P(A / Hi) |
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ɉɪɢɦɟɧɹɹ ɮɨɪɦɭɥɭ ɩɨɥɧɨɣ ɜɟɪɨɹɬɧɨɫɬɢ, ɩɨɥɭɱɢɦ:
P(A) P(H1) P(A / H1) P(H2 ) P(A / H2 ) P(H3 ) P(A / H3 )
P(H4 ) P(A / H4 );
P(A) 0, 25 0 0, 25 0,5 0, 25 1 0, 25 05 . 0, 25 (0 0,5 1 0,5) 0,5
Ɋɚɫɫɦɨɬɪɢɦ ɫɢɬɭɚɰɢɸ, ɩɪɨɬɢɜɨɩɨɥɨɠɧɭɸ ɩɪɟɞɵɞɭɳɟɣ (ɜ ɧɟɤɨɬɨɪɨɦ ɫɦɵɫɥɟ). ɉɭɫɬɶ ɫɨɛɵɬɢɟ Ⱥ ɭɠɟ ɩɪɨɢɡɨɲɥɨ. Ɉɩɪɟɞɟɥɢɦ ɜɟɪɨɹɬɧɨɫɬɶ ɬɨɝɨ, ɱɬɨ ɫɨɛɵɬɢɟ Ⱥ ɩɪɨɢɡɨɲɥɨ ɢɦɟɧɧɨ ɫ ɝɢɩɨɬɟɡɨɣ Hi . ɍɫɥɨɜɧɚɹ ɜɟɪɨɹɬɧɨɫɬɶ ɝɢɩɨɬɟɡɵ Hi , ɩɪɢ ɭɫɥɨɜɢɢ ɬɨɝɨ, ɱɬɨ ɫɨɛɵɬɢɟ Ⱥ ɭɠɟ ɩɪɨɢɡɨɲɥɨ, ɨɩɪɟɞɟɥɹɟɬɫɹ ɩɨ ɮɨɪɦɭɥɟ Ȼɚɣɟɫɚ:
P(Hi / A) |
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Ɂɚɦɟɬɢɦ, ɱɬɨ ɡɧɚɦɟɧɚɬɟɥɟɦ ɮɨɪɦɭɥɵ Ȼɚɣɟɫɚ ɹɜɥɹɟɬɫɹ ɮɨɪɦɭɥɚ ɩɨɥɧɨɣ ɜɟɪɨɹɬɧɨɫɬɢ:
n
¦P(Hi ) P(A / Hi ) .
i 1
Ɏɨɪɦɭɥɚ Ȼɚɣɟɫɚ ɱɚɫɬɨ ɢɧɬɟɪɩɪɟɬɢɪɭɟɬɫɹ ɤɚɤ ɮɨɪɦɭɥɚ, ɩɨɡɜɨɥɹɸɳɚɹ ɩɨ ɚɩɪɢɨɪɧɵɦ (ɢɡɜɟɫɬɧɵɦ ɞɨ ɩɪɨɜɟɞɟɧɢɹ ɨɩɵɬɚ) ɜɟɪɨɹɬɧɨɫɬɹɦ ɝɢɩɨɬɟɡP(Hi ) ɢ ɭɫɥɨɜɧɵɦ ɜɟɪɨɹɬɧɨɫɬɹɦ P(A / Hi ) ɜɵɱɢɫɥɢɬɶ ɚɩɨɫɬɟ-
ɪɢɨɪɧɵɟ (ɧɚɣɞɟɧɧɵɟ ɩɨɫɥɟ ɨɩɵɬɚ, ɬ.ɟ. ɩɪɢ ɭɫɥɨɜɢɢ, ɱɬɨ ɫɨɛɵɬɢɟ Ⱥ ɭɠɟ ɩɪɨɢɡɨɲɥɨ) ɜɟɪɨɹɬɧɨɫɬɢ P(Hi / A) .
ɉɪɢɦɟɪ 59. ɉɭɫɬɶ ɫɨɯɪɚɧɹɸɬɫɹ ɭɫɥɨɜɢɹ ɩɪɢɦɟɪɚ 58, ɧɨ ɞɨɩɨɥɧɢɬɟɥɶɧɨ ɢɡɜɟɫɬɧɨ, ɱɬɨ ɫɨɛɵɬɢɟ Ⱥ ɭɠɟ ɩɪɨɢɡɨɲɥɨ (ɩɭɬɧɢɤ ɩɨɩɚɥ ɢɡ
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ɩɭɧɤɬɚ Ɉ ɜ ɩɭɧɤɬ Ⱥ). Ʉɚɤɨɜɚ ɜɟɪɨɹɬɧɨɫɬɶ ɬɨɝɨ, ɱɬɨ ɨɧ ɜɵɛɪɚɥ ɞɨɪɨɝɭ, ɩɪɨɯɨɞɹɳɭɸ ɱɟɪɟɡ ɩɭɧɤɬ H4 (ɛɵɥɚ ɪɟɚɥɢɡɨɜɚɧɚ ɝɢɩɨɬɟɡɚ H4 )?
ɂɫɩɨɥɶɡɭɹ ɮɨɪɦɭɥɭ Ȼɚɣɟɫɚ, ɧɚɯɨɞɢɦ:
P(H4 |
/ A) |
P(H4 ) P(A / H4 ) |
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0, 25 0,5 |
0, 25 . |
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0,5 |
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ɉɪɢɦɟɪ 60. ɋɬɪɟɥɤɨɜɵɣ ɤɥɭɛ ɩɨɥɭɱɢɥ 12 ɜɢɧɬɨɜɨɤ, ɢɡ ɤɨɬɨɪɵɯ 8 ɩɪɢɫɬɪɟɥɹɧɧɵɯ, ɚ 4 ɧɟɬ. ȼɟɪɨɹɬɧɨɫɬɶ ɩɨɩɚɞɚɧɢɹ ɜ ɰɟɥɶ ɢɡ ɩɪɢɫɬɪɟɥɹɧɧɨɣ ɜɢɧɬɨɜɤɢ ɪɚɜɧɚ 0,8, ɚ ɢɡ ɧɟ ɩɪɢɫɬɪɟɥɹɧɧɨɣ 0,5. ɋɬɪɟɥɨɤ ɞɟɥɚɟɬ ɨɞɢɧ ɜɵɫɬɪɟɥ ɢɡ ɜɢɧɬɨɜɤɢ. ɇɚɣɞɟɦ ɜɟɪɨɹɬɧɨɫɬɶ ɬɨɝɨ, ɱɬɨ:
1)ɫɬɪɟɥɨɤ ɩɨɩɚɥ ɜ ɰɟɥɶ, ɜɵɛɪɚɜ ɜɢɧɬɨɜɤɭ ɧɚɭɝɚɞ;
2)ɟɫɥɢ ɫɬɪɟɥɨɤ ɩɨɩɚɥ ɜ ɰɟɥɶ, ɜɵɛɪɚɜ ɜɢɧɬɨɜɤɭ ɧɚɭɝɚɞ, ɬɨ ɨɧ ɫɬɪɟɥɹɥ ɢɡ ɩɪɢɫɬɪɟɥɹɧɧɨɣ ɜɢɧɬɨɜɤɢ.
ɋɨɛɵɬɢɟ Ⱥ — ɫɬɪɟɥɨɤ ɩɨɪɚɡɢɥ ɰɟɥɶ, ɜɵɛɪɚɜ ɜɢɧɬɨɜɤɭ ɧɚɭɝɚɞ. Ƚɢɩɨɬɟɡɚ H1 — ɫɬɪɟɥɨɤ ɜɨɡɶɦɟɬ ɩɪɢɫɬɪɟɥɹɧɧɭɸ ɜɢɧɬɨɜɤɭ.
Ƚɢɩɨɬɟɡɚ H2 — ɫɬɪɟɥɨɤ ɜɨɡɶɦɟɬ ɧɟ ɩɪɢɫɬɪɟɥɹɧɧɭɸ ɜɢɧɬɨɜɤɭ.
Ɉɱɟɜɢɞɧɨ, ɱɬɨ ɞɚɧɧɵɟ ɝɢɩɨɬɟɡɵ ɨɛɪɚɡɭɸɬ ɩɨɥɧɭɸ ɝɪɭɩɩɭ ɧɟɫɨɜɦɟɫɬɧɵɯ ɫɨɛɵɬɢɣ. ɉɪɢɦɟɧɹɹ ɤɥɚɫɫɢɱɟɫɤɨɟ ɨɩɪɟɞɟɥɟɧɢɟ ɜɟɪɨɹɬɧɨɫɬɢ, ɧɚɯɨɞɢɦ:
P(H1) |
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8 |
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0,67 |
— ɜɟɪɨɹɬɧɨɫɬɶ ɬɨɝɨ, ɱɬɨ ɜɢɧɬɨɜɤɚ ɩɪɢɫɬɪɟ- |
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ɥɹɧɧɚɹ; |
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P(H2 ) |
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4 |
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0,33 |
— ɜɟɪɨɹɬɧɨɫɬɶ ɬɨɝɨ, ɱɬɨ ɜɢɧɬɨɜɤɚ ɧɟ ɩɪɢ- |
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ɫɬɪɟɥɹɧɧɚɹ.
ɋɞɟɥɚɟɦ ɩɪɨɜɟɪɤɭ (ɫɭɦɦɚ ɜɟɪɨɹɬɧɨɫɬɟɣ ɫɨɛɵɬɢɣ, ɨɛɪɚɡɭɸɳɢɯ ɩɨɥɧɭɸ ɝɪɭɩɩɭ, ɟɫɬɶ ɫɨɛɵɬɢɟ ɞɨɫɬɨɜɟɪɧɨɟ):
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P(H1) P(H2 ) |
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8 |
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4 |
1. |
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12 |
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12 |
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ɋɨɝɥɚɫɧɨ ɭɫɥɨɜɢɸ ɡɚɞɚɱɢ ɡɚɩɢɲɟɦ ɭɫɥɨɜɧɵɟ ɜɟɪɨɹɬɧɨɫɬɢ ɩɨɩɚɞɚ- |
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ɧɢɹ ɫɬɪɟɥɤɨɦ ɜ ɰɟɥɶ: |
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P(A / H1) |
0,8 — ɜɟɪɨɹɬɧɨɫɬɶ ɩɨɩɚɫɬɶ ɜ ɰɟɥɶ, ɟɫɥɢ ɫɬɪɟɥɨɤ ɜɵɛɢ- |
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ɪɚɟɬ ɩɪɢɫɬɪɟɥɹɧɧɭɸ ɜɢɧɬɨɜɤɭ; |
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P(A / H2 ) |
0,5 — ɜɟɪɨɹɬɧɨɫɬɶ ɩɨɩɚɫɬɶ ɜ ɰɟɥɶ, ɟɫɥɢ ɫɬɪɟɥɨɤ ɜɵɛɢ- |
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ɪɚɟɬ ɧɟ ɩɪɢɫɬɪɟɥɹɧɧɭɸ ɜɢɧɬɨɜɤɭ.
1. ɉɪɢɦɟɧɹɹ ɮɨɪɦɭɥɭ ɩɨɥɧɨɣ ɜɟɪɨɹɬɧɨɫɬɢ, ɧɚɯɨɞɢɦ ɜɟɪɨɹɬɧɨɫɬɶ ɬɨɝɨ, ɱɬɨ ɫɬɪɟɥɨɤ ɩɨɩɚɥ ɜ ɰɟɥɶ, ɜɵɛɪɚɜ ɜɢɧɬɨɜɤɭ ɧɚɭɝɚɞ:
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P(A) P(H1) P(A / H1) P(H2 ) P(A / H2 ) 0,67 0,8 0,33 0,5 0,701.
2. ɉɪɢɦɟɧɹɹ ɮɨɪɦɭɥɭ Ȼɚɣɟɫɚ, ɧɚɯɨɞɢɦ ɜɟɪɨɹɬɧɨɫɬɶ ɬɨɝɨ, ɱɬɨ ɟɫɥɢ ɫɬɪɟɥɨɤ ɩɨɩɚɥ ɜ ɰɟɥɶ, ɜɵɛɪɚɜ ɜɢɧɬɨɜɤɭ ɧɚɭɝɚɞ, ɬɨ ɨɧ ɫɬɪɟɥɹɥ ɢɡ ɩɪɢɫɬɪɟɥɹɧɧɨɣ ɜɢɧɬɨɜɤɢ:
P(H1 |
/ A) |
P(H1) P(A / H1) |
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0,67 0,8 |
0,76 . |
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0,701 |
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ɉɪɢɦɟɪ 61. ɂɦɟɟɬɫɹ ɬɪɢ ɨɞɢɧɚɤɨɜɵɯ ɫɭɧɞɭɤɚ. ȼ ɩɟɪɜɨɦ ɫɭɧɞɭɤɟ ɧɚɯɨɞɹɬɫɹ ɞɜɟ ɫɟɪɟɛɪɹɧɵɟ ɦɨɧɟɬɵ, ɜɨ ɜɬɨɪɨɦ ɞɜɟ ɡɨɥɨɬɵɟ ɦɨɧɟɬɵ, ɚ ɜ ɬɪɟɬɶɟɦ ɨɞɧɚ ɡɨɥɨɬɚɹ ɦɨɧɟɬɚ ɢ ɨɞɧɚ ɫɟɪɟɛɪɹɧɚɹ. ɇɚɭɝɚɞ ɜɵɛɪɚɥɢ ɫɭɧɞɭɤ ɢ ɜɵɧɭɥɢ ɢɡ ɧɟɝɨ ɨɞɧɭ ɦɨɧɟɬɭ. Ɇɨɧɟɬɚ ɨɤɚɡɚɥɚɫɶ ɡɨɥɨɬɨɣ. Ʉɚɤɨɜɚ ɜɟɪɨɹɬɧɨɫɬɶ ɬɨɝɨ, ɱɬɨ ɜɬɨɪɚɹ ɦɨɧɟɬɚ ɜ ɷɬɨɦ ɫɭɧɞɭɤɟ ɬɨɠɟ ɡɨɥɨɬɚɹ?
ɋɨɛɵɬɢɟ Ⱥ — ɜɵɧɭɥɢ ɡɨɥɨɬɭɸ ɦɨɧɟɬɭ, ɜɵɛɪɚɜ ɫɭɧɞɭɤ ɧɚɭɝɚɞ. Ƚɢɩɨɬɟɡɚ H1 — ɜɵɛɪɚɥɢ ɩɟɪɜɵɣ ɫɭɧɞɭɤ.
Ƚɢɩɨɬɟɡɚ H2 — ɜɵɛɪɚɥɢ ɜɬɨɪɨɣ ɫɭɧɞɭɤ.
Ƚɢɩɨɬɟɡɚ H3 — ɜɵɛɪɚɥɢ ɬɪɟɬɢɣ ɫɭɧɞɭɤ.
Ɉɱɟɜɢɞɧɨ, ɱɬɨ ɞɚɧɧɵɟ ɝɢɩɨɬɟɡɵ ɪɚɜɧɨɜɟɪɨɹɬɧɵ (ɫɭɧɞɭɤɢ ɫɱɢɬɚɸɬɫɹ ɨɞɢɧɚɤɨɜɵɦɢ) ɢ ɨɛɪɚɡɭɸɬ ɩɨɥɧɭɸ ɝɪɭɩɩɭ ɧɟɫɨɜɦɟɫɬɧɵɯ ɫɨɛɵɬɢɣ.
1 P(H1) P(H2 ) P(H3 ) 3 .
ɋɞɟɥɚɟɦ ɩɪɨɜɟɪɤɭ (ɫɭɦɦɚ ɜɟɪɨɹɬɧɨɫɬɟɣ ɫɨɛɵɬɢɣ, ɨɛɪɚɡɭɸɳɢɯ ɩɨɥɧɭɸ ɝɪɭɩɩɭ, ɟɫɬɶ ɫɨɛɵɬɢɟ ɞɨɫɬɨɜɟɪɧɨɟ):
P(H1) P(H2 ) P(H3 ) |
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Ɂɧɚɹ ɧɚɛɨɪ ɦɨɧɟɬ ɜ ɤɚɠɞɨɦ ɫɭɧɞɭɤɟ, ɥɟɝɤɨ ɨɩɪɟɞɟɥɢɬɶ ɜɟɪɨɹɬɧɨɫɬɢ ɜɵɧɭɬɶ ɡɨɥɨɬɭɸ ɦɨɧɟɬɭ ɢɡ ɩɟɪɜɨɝɨ, ɜɬɨɪɨɝɨ ɢ ɬɪɟɬɶɟɝɨ ɫɭɧɞɭɤɚ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ:
P(A / H1) |
0 — ɜɟɪɨɹɬɧɨɫɬɶ ɜɵɧɭɬɶ ɡɨɥɨɬɭɸ ɦɨɧɟɬɭ, ɟɫɥɢ ɧɚɭɝɚɞ |
ɜɵɛɪɚɧ ɩɟɪɜɵɣ ɫɭɧɞɭɤ; |
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P(A / H2 ) |
1 — ɜɟɪɨɹɬɧɨɫɬɶ ɜɵɧɭɬɶ ɡɨɥɨɬɭɸ ɦɨɧɟɬɭ, ɟɫɥɢ ɧɚɭɝɚɞ |
ɜɵɛɪɚɧ ɜɬɨɪɨɣ ɫɭɧɞɭɤ; |
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P(A / H3 ) |
0,5 — ɜɟɪɨɹɬɧɨɫɬɶ ɜɵɧɭɬɶ ɡɨɥɨɬɭɸ ɦɨɧɟɬɭ, ɟɫɥɢ ɧɚɭ- |
ɝɚɞ ɜɵɛɪɚɧ ɬɪɟɬɢɣ ɫɭɧɞɭɤ.
ɇɚɣɞɟɧɧɵɟ ɜɟɪɨɹɬɧɨɫɬɢ ɭɞɨɛɧɨ ɡɚɩɢɫɚɬɶ ɜ ɬɚɛɥ. 4.2.
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ǺȈȉȓȐȞȈ 4.2
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P(Hi ) |
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ɋɨɝɥɚɫɧɨ ɭɫɥɨɜɢɸ ɡɚɞɚɱɢ ɫɨɛɵɬɢɟ Ⱥ ɭɠɟ ɩɪɨɢɡɨɲɥɨ — ɡɨɥɨɬɭɸ ɦɨɧɟɬɭ ɜɵɧɭɥɢ. Ɍɪɟɛɭɟɬɫɹ ɨɩɪɟɞɟɥɢɬɶ ɜɟɪɨɹɬɧɨɫɬɶ ɬɨɝɨ, ɱɬɨ ɡɨɥɨɬɭɸ ɦɨɧɟɬɭ ɜɵɧɭɥɢ ɢɦɟɧɧɨ ɢɡ ɜɬɨɪɨɝɨ ɫɭɧɞɭɤɚ (ɬɚɤ ɤɚɤ ɬɨɥɶɤɨ ɜɨ ɜɬɨɪɨɦ ɫɭɧɞɭɤɟ ɨɫɬɚɥɚɫɶ ɟɳɟ ɨɞɧɚ ɡɨɥɨɬɚɹ ɦɨɧɟɬɚ). ɉɪɢɦɟɧɹɹ ɮɨɪɦɭɥɭ Ȼɚɣɟɫɚ, ɧɚɯɨɞɢɦ:
P(H2 / A) |
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P(H1) P(A / H1) P(H2 ) P(A / H2 ) P(H3 ) P(A / H3 ) |
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ɉɪɢɦɟɪ 62. 30% ɩɚɰɢɟɧɬɨɜ, ɩɨɫɬɭɩɢɜɲɢɯ ɜ ɛɨɥɶɧɢɰɭ, ɩɪɢɧɚɞɥɟɠɚɬ ɩɟɪɜɨɣ ɫɨɰɢɚɥɶɧɨɣ ɝɪɭɩɩɟ, 20% — ɜɬɨɪɨɣ ɢ 50% — ɬɪɟɬɶɟɣ. ȼɟɪɨɹɬɧɨɫɬɶ ɡɚɛɨɥɟɜɚɧɢɹ ɬɭɛɟɪɤɭɥɟɡɨɦ ɞɥɹ ɩɪɟɞɫɬɚɜɢɬɟɥɹ ɤɚɠɞɨɣ ɫɨɰɢɚɥɶɧɨɣ ɝɪɭɩɩɵ ɪɚɜɧɚ 0,02, 0,03 ɢ 0,01 ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ. ɋɥɭɱɚɣɧɵɦ ɨɛɪɚɡɨɦ ɜɵɛɪɚɥɢ ɩɚɰɢɟɧɬɚ ɢ ɩɪɨɜɟɥɢ ɨɛɫɥɟɞɨɜɚɧɢɟ, ɤɨɬɨɪɨɟ ɩɨɤɚɡɚɥɨ ɧɚɥɢɱɢɟ ɬɭɛɟɪɤɭɥɟɡɚ. ɇɚɣɞɟɦ ɜɟɪɨɹɬɧɨɫɬɶ ɬɨɝɨ, ɱɬɨ ɩɚɰɢɟɧɬ ɩɪɢɧɚɞɥɟɠɢɬ ɤ ɬɪɟɬɶɟɣ ɫɨɰɢɚɥɶɧɨɣ ɝɪɭɩɩɟ.
ɋɨɛɵɬɢɟ Ⱥ — ɫɥɭɱɚɣɧɨ ɜɵɛɪɚɧɧɵɣ ɩɚɰɢɟɧɬ ɛɨɥɟɧ ɬɭɛɟɪɤɭɥɟɡɨɦ. Ƚɢɩɨɬɟɡɚ H1 — ɩɚɰɢɟɧɬ ɩɪɢɧɚɞɥɟɠɢɬ ɤ ɩɟɪɜɨɣ ɫɨɰɢɚɥɶɧɨɣ
ɝɪɭɩɩɟ.
Ƚɢɩɨɬɟɡɚ H2 — ɩɚɰɢɟɧɬ ɩɪɢɧɚɞɥɟɠɢɬ ɤɨ ɜɬɨɪɨɣ ɫɨɰɢɚɥɶɧɨɣ
ɝɪɭɩɩɟ.
Ƚɢɩɨɬɟɡɚ H3 — ɩɚɰɢɟɧɬ ɩɪɢɧɚɞɥɟɠɢɬ ɤ ɬɪɟɬɶɟɣ ɫɨɰɢɚɥɶɧɨɣ
ɝɪɭɩɩɟ.
Ɉɱɟɜɢɞɧɨ, ɱɬɨ ɞɚɧɧɵɟ ɝɢɩɨɬɟɡɵ ɨɛɪɚɡɭɸɬ ɩɨɥɧɭɸ ɝɪɭɩɩɭ ɧɟɫɨɜɦɟɫɬɧɵɯ ɫɨɛɵɬɢɣ. ɉɪɢɦɟɧɹɹ ɤɥɚɫɫɢɱɟɫɤɨɟ ɨɩɪɟɞɟɥɟɧɢɟ ɜɟɪɨɹɬɧɨɫɬɢ, ɧɚɯɨɞɢɦ:
108
P(H1) |
m |
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30% |
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0,3 |
— ɜɟɪɨɹɬɧɨɫɬɶ ɬɨɝɨ, ɱɬɨ ɩɚɰɢɟɧɬ ɩɪɢɧɚɞ- |
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n |
100% |
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ɥɟɠɢɬ ɤ ɩɟɪɜɨɣ ɫɨɰɢɚɥɶɧɨɣ ɝɪɭɩɩɟ; |
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P(H2 ) |
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m |
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20% |
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0, 2 |
— ɜɟɪɨɹɬɧɨɫɬɶ ɬɨɝɨ, ɱɬɨ ɩɚɰɢɟɧɬ ɩɪɢɧɚɞ- |
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n |
100% |
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ɥɟɠɢɬ ɤɨ ɜɬɨɪɨɣ ɫɨɰɢɚɥɶɧɨɣ ɝɪɭɩɩɟ; |
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P(H3 ) |
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m |
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50% |
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0,5 |
— ɜɟɪɨɹɬɧɨɫɬɶ ɬɨɝɨ, ɱɬɨ ɩɚɰɢɟɧɬ ɩɪɢɧɚɞ- |
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n |
100% |
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ɥɟɠɢɬ ɤ ɬɪɟɬɶɟɣ ɫɨɰɢɚɥɶɧɨɣ ɝɪɭɩɩɟ.
ɋɞɟɥɚɟɦ ɩɪɨɜɟɪɤɭ (ɫɭɦɦɚ ɜɟɪɨɹɬɧɨɫɬɟɣ ɫɨɛɵɬɢɣ, ɨɛɪɚɡɭɸɳɢɯ ɩɨɥɧɭɸ ɝɪɭɩɩɭ, ɟɫɬɶ ɫɨɛɵɬɢɟ ɞɨɫɬɨɜɟɪɧɨɟ):
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P(H1) P(H2 ) P(H3 ) 0,3 0, 2 0,5 1. |
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Ɂɚɩɢɲɟɦ ɭɫɥɨɜɧɵɟ ɜɟɪɨɹɬɧɨɫɬɢ ɬɨɝɨ, ɱɬɨ ɫɥɭɱɚɣɧɨ ɜɵɛɪɚɧɧɵɣ |
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ɩɚɰɢɟɧɬ ɛɨɥɟɧ ɬɭɛɟɪɤɭɥɟɡɨɦ: |
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P(A / H1) |
0,02 — ɜɟɪɨɹɬɧɨɫɬɶ ɬɨɝɨ, ɱɬɨ ɫɥɭɱɚɣɧɵɣ ɩɚɰɢɟɧɬ ɛɨɥɟɧ |
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ɬɭɛɟɪɤɭɥɟɡɨɦ, ɟɫɥɢ ɨɧ ɩɪɢɧɚɞɥɟɠɢɬ ɤ ɩɟɪɜɨɣ ɫɨɰɢɚɥɶɧɨɣ ɝɪɭɩɩɟ; |
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P(A / H2 ) |
0,03 — ɜɟɪɨɹɬɧɨɫɬɶ ɬɨɝɨ, ɱɬɨ ɫɥɭɱɚɣɧɵɣ ɩɚɰɢɟɧɬ ɛɨɥɟɧ |
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ɬɭɛɟɪɤɭɥɟɡɨɦ, ɟɫɥɢ ɨɧ ɩɪɢɧɚɞɥɟɠɢɬ ɤɨ ɜɬɨɪɨɣ ɫɨɰɢɚɥɶɧɨɣ ɝɪɭɩɩɟ; |
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P(A / H3 ) |
0,01 — ɜɟɪɨɹɬɧɨɫɬɶ ɬɨɝɨ, ɱɬɨ ɫɥɭɱɚɣɧɵɣ ɩɚɰɢɟɧɬ ɛɨɥɟɧ |
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ɬɭɛɟɪɤɭɥɟɡɨɦ, ɟɫɥɢ ɨɧ ɩɪɢɧɚɞɥɟɠɢɬ ɤ ɬɪɟɬɶɟɣ ɫɨɰɢɚɥɶɧɨɣ ɝɪɭɩɩɟ. |
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ɇɚɣɞɟɧɧɵɟ ɜɟɪɨɹɬɧɨɫɬɢ ɭɞɨɛɧɨ ɡɚɩɢɫɚɬɶ ɜ ɬɚɛɥ. 4.3. |
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ǺȈȉȓȐȞȈ 4.3 |
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i |
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1 |
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2 |
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3 |
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P(Hi ) |
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0,3 |
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0,2 |
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0,5 |
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P(A / Hi) |
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0,02 |
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0,03 |
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0,01 |
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ɋɨɝɥɚɫɧɨ ɭɫɥɨɜɢɸ ɡɚɞɚɱɢ ɫɨɛɵɬɢɟ Ⱥ ɭɠɟ ɩɪɨɢɡɨɲɥɨ — ɫɥɭɱɚɣɧɨ ɜɵɛɪɚɧɧɵɣ ɩɚɰɢɟɧɬ ɛɨɥɟɧ ɬɭɛɟɪɤɭɥɟɡɨɦ. Ɍɪɟɛɭɟɬɫɹ ɨɩɪɟɞɟɥɢɬɶ ɜɟɪɨɹɬɧɨɫɬɶ, ɱɬɨ ɩɚɰɢɟɧɬ ɩɪɢɧɚɞɥɟɠɢɬ ɢɦɟɧɧɨ ɤ ɬɪɟɬɶɟɣ ɫɨɰɢɚɥɶɧɨɣ ɝɪɭɩɩɟ. ɉɪɢɦɟɧɹɹ ɮɨɪɦɭɥɭ Ȼɚɣɟɫɚ, ɧɚɯɨɞɢɦ:
P(H3 / A) |
P(H3 ) P(A / H3 ) |
; |
P(H1) P(A / H1) P(H2 ) P(A / H2 ) P(H3 ) P(A / H3 ) |
109
P(H3 / A) |
0,5 0,01 |
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5 |
. |
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0,3 0,02 0, 2 0,03 0,5 0,01 |
17 |
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ɉɪɢɦɟɪ 63 . ɉɨ ɩɪɟɞɦɟɬɭ ɦɚɬɟɦɚɬɢɤɚ ɢ ɢɧɮɨɪɦɚɬɢɤɚ ɢɦɟɟɬɫɹ 30 ɷɤɡɚɦɟɧɚɰɢɨɧɧɵɯ ɛɢɥɟɬɨɜ. ɋɬɭɞɟɧɬ Ɋɨɦɚɧɨɜ ɜɵɭɱɢɥ ɬɨɥɶɤɨ 20. Ʉɚɤɢɦ ɩɨ ɫɱɟɬɭ ɥɭɱɲɟ ɟɦɭ ɫɞɚɜɚɬɶ ɷɤɡɚɦɟɧ — ɩɟɪɜɵɦ ɢɥɢ ɜɬɨɪɵɦ?
ɋɨɛɵɬɢɟ Ⱥ — ɫɬɭɞɟɧɬ Ɋɨɦɚɧɨɜ ɡɚɯɨɞɢɬ ɩɟɪɜɵɦ ɢ ɭɫɩɟɲɧɨ ɫɞɚɟɬ
ɷɤɡɚɦɟɧ. P(A) |
20 |
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2 |
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30 |
3 |
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ɋɨɛɵɬɢɟ B — ɫɬɭɞɟɧɬ Ɋɨɦɚɧɨɜ ɡɚɯɨɞɢɬ ɜɬɨɪɵɦ ɢ ɭɫɩɟɲɧɨ ɫɞɚɟɬ ɷɤɡɚɦɟɧ. ɋɨɛɵɬɢɟ B ɦɨɠɟɬ ɩɪɨɢɡɨɣɬɢ ɬɨɥɶɤɨ ɫ ɨɞɧɨɣ ɢɡ ɝɢɩɨɬɟɡ
H1 , H2 .
Ƚɢɩɨɬɟɡɚ H1 — ɫɬɭɞɟɧɬ, ɤɨɬɨɪɵɣ ɫɞɚɟɬ ɷɤɡɚɦɟɧ ɩɟɪɜɵɦ (ɩɟɪɟɞ
Ɋɨɦɚɧɨɜɵɦ) ɜɵɬɚɳɢɬ 1 ɢɡ 20 ɛɢɥɟɬɨɜ, ɤɨɬɨɪɵɟ Ɋɨɦɚɧɨɜ ɡɧɚɟɬ. Ƚɢɩɨɬɟɡɚ H2 — ɫɬɭɞɟɧɬ, ɤɨɬɨɪɵɣ ɫɞɚɟɬ ɷɤɡɚɦɟɧ ɩɟɪɜɵɦ (ɩɟɪɟɞ
Ɋɨɦɚɧɨɜɵɦ) ɜɵɬɚɳɢɬ 1 ɢɡ 10 ɛɢɥɟɬɨɜ, ɤɨɬɨɪɵɟ Ɋɨɦɚɧɨɜ ɧɟ ɡɧɚɟɬ. Ɉɱɟɜɢɞɧɨ, ɱɬɨ ɞɚɧɧɵɟ ɝɢɩɨɬɟɡɵ ɨɛɪɚɡɭɸɬ ɩɨɥɧɭɸ ɝɪɭɩɩɭ ɧɟɫɨ-
ɜɦɟɫɬɧɵɯ ɫɨɛɵɬɢɣ. ɉɪɢɦɟɧɹɹ ɤɥɚɫɫɢɱɟɫɤɨɟ ɨɩɪɟɞɟɥɟɧɢɟ ɜɟɪɨɹɬɧɨɫɬɢ, ɧɚɯɨɞɢɦ:
P(H1) |
m |
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20 |
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2 |
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— ɜɟɪɨɹɬɧɨɫɬɶ ɬɨɝɨ, ɱɬɨ ɩɪɟɞɵɞɭɳɢɣ ɫɬɭɞɟɧɬ |
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n |
30 |
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3 |
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ɜɵɬɚɳɢɬ 1 ɢɡ 20 ɛɢɥɟɬɨɜ, ɤɨɬɨɪɵɟ Ɋɨɦɚɧɨɜ ɡɧɚɟɬ; |
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P(H2 ) |
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m |
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10 |
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1 |
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— ɜɟɪɨɹɬɧɨɫɬɶ ɬɨɝɨ, ɱɬɨ ɩɪɟɞɵɞɭɳɢɣ ɫɬɭɞɟɧɬ |
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n |
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30 |
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3 |
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ɜɵɬɚɳɢɬ 1 ɢɡ 10 ɛɢɥɟɬɨɜ, ɤɨɬɨɪɵɟ Ɋɨɦɚɧɨɜ ɧɟ ɡɧɚɟɬ.
ɋɞɟɥɚɟɦ ɩɪɨɜɟɪɤɭ (ɫɭɦɦɚ ɜɟɪɨɹɬɧɨɫɬɟɣ ɫɨɛɵɬɢɣ, ɨɛɪɚɡɭɸɳɢɯ
ɩɨɥɧɭɸ ɝɪɭɩɩɭ, ɟɫɬɶ ɫɨɛɵɬɢɟ ɞɨɫɬɨɜɟɪɧɨɟ): P(H1) P(H2 ) |
2 |
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1 . |
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3 |
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3 |
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ɋɨɝɥɚɫɧɨ ɭɫɥɨɜɢɸ ɩɪɢɦɟɪɚ ɡɚɩɢɲɟɦ ɭɫɥɨɜɧɵɟ ɜɟɪɨɹɬɧɨɫɬɢ ɭɫ- |
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ɩɟɲɧɨɣ ɫɞɚɱɢ ɷɤɡɚɦɟɧɚ, ɟɫɥɢ Ɋɨɦɚɧɨɜ ɫɞɚɟɬ ɜɬɨɪɵɦ: |
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P(B / H1) |
19 |
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— ɜɟɪɨɹɬɧɨɫɬɶ ɭɫɩɟɲɧɨ ɫɞɚɬɶ ɷɤɡɚɦɟɧ, ɟɫɥɢ ɩɪɟɞɵ- |
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29 |
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ɞɭɳɢɣ ɫɬɭɞɟɧɬ ɜɵɬɚɳɢɬ 1 ɢɡ 20 ɛɢɥɟɬɨɜ, ɤɨɬɨɪɵɟ Ɋɨɦɚɧɨɜ ɡɧɚɟɬ; |
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P(B / H2 ) |
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20 |
— ɜɟɪɨɹɬɧɨɫɬɶ ɭɫɩɟɲɧɨ ɫɞɚɬɶ ɷɤɡɚɦɟɧ, ɟɫɥɢ ɩɪɟɞɵ- |
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29 |
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ɞɭɳɢɣ ɫɬɭɞɟɧɬ ɜɵɬɚɳɢɬ 1 ɢɡ 10 ɛɢɥɟɬɨɜ, ɤɨɬɨɪɵɟ Ɋɨɦɚɧɨɜ ɧɟ ɡɧɚɟɬ. ɉɪɢɦɟɧɹɹ ɮɨɪɦɭɥɭ ɩɨɥɧɨɣ ɜɟɪɨɹɬɧɨɫɬɢ, ɧɚɯɨɞɢɦ ɜɟɪɨɹɬɧɨɫɬɶ ɬɨ-
ɝɨ, ɱɬɨ Ɋɨɦɚɧɨɜ ɭɫɩɟɲɧɨ ɫɞɚɫɬ ɷɤɡɚɦɟɧ, ɟɫɥɢ ɡɚɣɞɟɬ ɜɬɨɪɵɦ:
110