ryer manufacturer parchases heating elements from three different suppliers: Agr

Question

ryer manufacturer parchases heating elements from three different suppliers: Agrostat, rock, and Thermtek. Thirty percent of the heating elements are supplied by Argostat, 50 ent by Bermrock, and twe nty percent by Thermtek. The elements are mixed in a supply bin T0%of the Argostat elements are andjust 4% of those from inspection and installation . Based on past experience, defective compar ntek. An assembly worker randomly selects an element for installation .What is the Ther probability that element come from Thermtek and it happened to be non defective element? (Use Bayes' Theorem)

Explanation / Answer

We use the following notations:

A = Heating elements of Agrostat

B = Heating elements of Bermrock

C = Heating elements of Thermtek

D = Heating elements is defective

Let P(A) = 0.30 Because Argostat supplies 30% of heating elements

Let P(B) = 0.50 Because Bermrock supplies 50% of heating elements

Let P(C) = 0.20 Because Thermtek supplies 20% of heating elements

P(D/A) = 0.10 Because 10% of Argostat supplies are defective

P(D/B) = 0.05 Because 5% of Bermrock supplies are defective

P(D/C) = 0.04 Because 4% of Termtek supplies are defective

Here is a bayes theorem extended to include three events corresponding to the selection (A,B,C):

P(C/D) = [P(C)*P(D/C)]/{[P(A)*P(D/A)]+[P(B)*P(D/B)]+[P(C)*P(D/C)]}

= [0.20*0.04]/{[0.30*0.10]+[0.50*0.05]+[0.20*0.04]}

= 0.127 (rounded)

P(C/D) = 0.127 this is probability to be defective to find the non defective we should subtract the defective items from one i.e;

= 1- 0.127

= 0.873

Therefore the probability of the element came from Thermtek and it happens to be non defective heating element is 0.873

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