1. 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

2. 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 …

3. Your turn …
Problem 3, page 46

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

5. 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) = = 0.982
Entire system: P(1)P(2)P(E) = .855*.982*.97 =.814

6. 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 =

7. 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

8. Your turn …
Problem 3, page 54