A manufacturing company is considering the possibility of replacing an old piece of equipment with a...

 

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A manufacturing company is considering the possibility of replacing an old piece of equipment with a new piece of equipment. The new equipment may turn out to be reliable (labeled A) or unreliable (labeled A ). The probability of new equipment being reliable is P(A) = 0.6, and the probability of it being unreliable is P(Ā)= 0.4. If the new piece of equipment is reliable, the total return will be $155. If it is unreliable, the total return will be $35. The existing equipment (if not replaced) will have a total return of S76. All costs are in million dollars. The company can ask an expert to provide his/her opinion in regard to the reliability of the new piece of equipment. The expert charges S15 to render his opinion. The expert will either predict the equipment to be reliable (B) or to be unreliable (B). The company knows the following probabilities: B Total P(B|A)= 0.6 P(B|Ā) = 0.8 P(B|A)=0.4 P(BĀ)=0.2 A 1 a) Find all unknown conditional probabilities. b) Find the value of the expert opinion using expected value. Show decision trees for with and without expert opinion. c) Should the expert be hired? A manufacturing company is considering the possibility of replacing an old piece of equipment with a new piece of equipment. The new equipment may turn out to be reliable (labeled A) or unreliable (labeled A ). The probability of new equipment being reliable is P(A) = 0.6, and the probability of it being unreliable is P(Ā)= 0.4. If the new piece of equipment is reliable, the total return will be $155. If it is unreliable, the total return will be $35. The existing equipment (if not replaced) will have a total return of S76. All costs are in million dollars. The company can ask an expert to provide his/her opinion in regard to the reliability of the new piece of equipment. The expert charges S15 to render his opinion. The expert will either predict the equipment to be reliable (B) or to be unreliable (B). The company knows the following probabilities: B Total P(B|A)= 0.6 P(B|Ā) = 0.8 P(B|A)=0.4 P(BĀ)=0.2 A 1 a) Find all unknown conditional probabilities. b) Find the value of the expert opinion using expected value. Show decision trees for with and without expert opinion. c) Should the expert be hired?

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