Question

A dryer manufacturer purchases heating elements from three different suppliers: Argostat, Bermrock, and Thermtek. Thirty percent of the heating elements are supplied by Arostat, 50% by Bermrock, and 20% by Themtek. The elements are mixed in a supply bin prior to inspection and installation. Based on past experience, 10% of the Argostat elements are defective, compared to only 5% of those supplied by Bermrock, and just 4% of those from Thermtek. An assembly worker randomly selects an element for installation.

a) Contruct a probability tree to represent this problem.

b) What is the probability the element was supplied by Argostat?

c) What is the probability the element is Defective?

d) What is the probability the element was supplied by Thermtek and is Defective?

e) What is the probability the element was supplied by Thermtek or is not Defective?

f) If the heating element is Defective, what is the probability it was supplied by Argostat?

g) If the heating element is not Defective, what is the probability it was supplied by Bermrock?

Answer 1

let A , B and T are event of elements supplied by Argostat; Bermrock and Thermtek; also event of defective is D

a)

b)

probability the element was supplied by Argostat =0.30

c) probability the element is Defective =P(D)=P(A n D)+P(B n D)+P(T n D)=0.03+0.025+0.008 =0.063

d)

probability the element was supplied by Thermtek and is Defective =P(T n D)=0.008

e)

probability the element was supplied by Thermtek or is not Defective =P(T n Dc)=0.192

f)

P(A|D)=P(A n D)/P(D) =0.03/0.063=0.4762

g)

P(B|D^c)=P(B n D c)/P(Dc)=0.475/0.937=0.5069