E. A defibrillator manufacturer uses three different materials (Silver, Titanium
ID: 3070876 • Letter: E
Question
E. A defibrillator manufacturer uses three different materials (Silver, Titanium, and Copper) for the electrodes in its devices. Each electrode is made solely from a single material. The electrodes are designed as an adhesive pad, which must carry strong pulses of electricity without deteriorating and remain functional after 10 years. Events are defined as follows: . Ag: the electrode is made of Silver .Ti: the electrode is made of Titanium Cu: the electrode is made of Copper the electrode is functional after 10 years The probabilities that an electrode is made out of the different materials are as follows P(Ag) 0.2, P(Ti) 0.7, P(Cu) 0.1 and the conditional probabilities of functionality after 10 years are as follows: P(XIAg) = 0.9, P(XlTi) = 0.8, P(XCu) = 0.6 i. Using words, explain what P(Ag|X) represents. Then, compute P(AglX) ii Using words, explain what P(Ag'X) represents. Then, compute P(Ag'|X). iii. Using words, explain what P(X) represents. Then, compute P(X)Explanation / Answer
i) P(Ag/X) is represent the probabiltiy that functionality after 10 to the electorde is made of Silver.
By using Bayes theorem
P(Ag/x) = P(x/Ag) P(Ag) / [ P(x/Ag) P(Ag) + P(x/Ti) P(Ti) + P(x/Cu) P(Cu)]
= (0.9*0.2) / [0.9*0.2 + 0.8*0.7 + 0.1*0.6]
= 0.18 / 0.8 = 0.225
ii) P(Ag'/X) is represent the probabiltiy that functionality after 10 to the electorde is not made of Silver.
By using Bayes theorem
P(Ag'/x) = 1 - P(Ag/x) = 1 - 0.225 = 0.775
iii)
P(x) is represent is the probabiltiy that functionality after 10 is
P(x) = P(x/Ag) P(Ag) + P(x/Ti) P(Ti) + P(x/Cu) P(Cu)
= 0.9*0.2 + 0.8*0.7 + 0.1*0.6 = 0.8
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.