Applications of Probability Example: An appliance manufacturer has learned of an increased incidence of short circuits and fires in a line of ranges sold over a 5 month period. A review of the FMEA data indicates the probabilities that if a short circuit occurs, it will be at any one of several locations is as follows: Location P House Junction 0.46 Oven/MW junction 0.14 Thermostat 0.09 Oven coil 0.24 Electronic controls 0.07

Applications of Probability The probability that the short circuit does not occur at the house junction is … The probability that the short circuit occurs at either the Oven/MW junction or the oven coil is … The probability that both the electronic controls and the thermostat short circuit simultaneously is …

Your turn … Problem 3, page 46

Serial and Parallel Systems For increased safety and reliability, systems are often designed with redundancies. A typical system might look like the following:

Serial and Parallel Systems What is the probability that: Segment 1 works? Segment 2 works? The entire system works? 1 2 Segment 1: P(A∩B) = P(A)P(B) = (.95)(.9) = .855 Segment 2: 1 – P(C’)P(D’) = 1 – (.12)(.15) = 1-.018 = 0.982 Entire system: P(1)P(2)P(E) = .855*.982*.97 =.814

Conditional Probability If segment 2 works, what is the probability that component C does not work? P(C’∩D)/P(2) = ((1-.88)*0.85)/0.982 = 0.1039

Conditional Probability If the system works, what is the probability that component D does not work? P(A∩B∩C∩D’∩E)/P(System works) = (0.95*.9*.88*(1-.85)*.97)/0.814=0.1345

Your turn … Problem 3, page 54