BLASIANNkidd
16.01.2021 •
Mathematics
Tres maquinas (A,B,C) producen el 40 % , 35% y 25 % respectivamente , del total de las piezas manufacturadas en una fabrica .Los porcentajes de produccion defectuosa de estas maquinas son del 3% 4 % y 5 % respectivamente
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Ответ:
La probabilidad de que la pieza elegida sea defectuosa, P(D), 0.0385
La máquina con mayor probabilidad de haber producido la pieza defectuosa es A
Step-by-step explanation:
Sea D= "la pieza es defectuosa" y N= "la pieza no es defectuosa". La información del problema puede expresarse en el diagrama de árbol adjunto.
Para calcular la probabilidad de que la pieza elegida sea defectuosa, P(D), por la propiedad de la probabilidad total,
P(D) = P(A) · P(D/A) + P(B) · P(D/B) + P(C) · P(D/C) =
= 0.40 · 0.03 + 0.35 · 0.04 + 0.25 · 0.05 = 0.0385
Debemos calcular P(B/D). Por el teorema de Bayes,
P(B/D)=P(B) x P(D/B) / P(A) x P(D/A) + P(B) x P(D/B) +P(C) x P(D/C)
= 0.35 · 0.04 / 0.40 · 0.03 + 0.35 · 0.04 + 0.25 · 0.05
Calculamos P(A/D) y P(C/D), comparándolas con el valor de P(B/D) ya calculado. Aplicando el teorema de Bayes, obtenemos:
0.012
0.0385
P(A/D)= 0.311
0.014
0.0385
P(B(D)=0.363
0.0125
0.0385
P(C/D)=0.324
La máquina con mayor probabilidad de haber producido la pieza defectuosa es A
Ответ: