Applications of Probability

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:

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

6. Conditional Probability • If segment 2 works, what is the probability that component C does not work?

7. Conditional Probability • If the system works, what is the probability that component D does not work?

8. Your turn … • Problem 3, page 54