A system has two components that operate in parallel, as shown in the following

Question

A system has two components that operate in parallel, as shown in the following diagram. Because the components operate in parallel, at least one of the components must function properly if the system is to function properly. The probabilities of failures for the components 1 and 2 during one period of operation are 0.20 and 0.03, respectively. Let F1 denote the event that component 1 fails during one period of operation, and F2 denote the event that component 2 fails during one period of operation. The component failures are independent. The event corresponding to the above system functioning properly during one period of operation is F1 or F2. not F1 or not F2. F1 and F2. not F1 and not F2.

Explanation / Answer

a)P(F1 or F2)=P(F1)+P(F2)-P(F1 and F2) =0.2+0.03-0.2*0.03=0.23-0.006=0.224

b)P(not F1 or Not F2)=1-P(F1 and F2)=1-0.2*0.03=0.994

c)P(F1 and F2)=0.2*0.03=0.006

d)P(not F1 and not F2)=P(not F1)*P(not F2)=0.8*0.97=0.776

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.