The circuit below is made of 5 independent components as shown in the figure below.
PC1)=P(C2)=0.94
PC3)=0.97
P(C4)=P(C5)=085
The events C1 and C2 are independent
P(C1∩C2)=P(C1)P(C2) The events C4 and C5 are independent
P(C4∩C5)=P(C4)P(C5)
P(C1∪C2)=P(C1)+P(C2)−P(C1∩C2)
=P(C1)+P(C2)−P(C1)P(C2)
=0.94+0.94−0.94(0.94)=0.9964
P(C4∪C5)=P(C4)+P(C5)−P(C4∩C5)
=P(C4)+P(C5)−P(C4)P(C5)
=0.85+0.85−0.85(0.85)=0.9775
All five components are independent
P(work)=P((C1∪C2)∩C3∩(C4∪C5))
=0.9964(0.97)(0.9775)=0.94476157
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