Applications of Probability Example An appliance manufacturer has

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 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? 1 2 – Segment 2 works? – The entire system works?

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

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

Your turn … • Problem 3, page 54