Answer:
P(system) = p(subcomp1 ∩ subcomp2)
P(system) = 1.60 x 0.64
P(system) = 1.0240
Step-by-step explanation:
In the system we have 2 subsystem
Let say subsystem 1 and subsystem 2
Subsystem 1 consist of 2 components, component 1 and component 2 that subsystem 1 works if and only if either component 1 or component 2 work
I.e p(subcomp1) = p ( comp1 | comp2)
Since the P(component works) = 0.80
Therefore P(subcomp1) = p(comp1) + p(comp2)
= 0.80 + 0.80
P(subcomp1) = 1.60
Subsystem 2 consist of 2 components, component 3 and component 4 that subsystem 2 works if and only if both component 3 and component 4 work
I.e p(subcomp2) = p ( comp3 ∩ comp4)
Since the P(component works) = 0.80
Therefore P(subcomp2) = p(comp3) x p(comp4)
= 0.80 x 0.80
P(subcomp2) = 0.64
Therefore since the component are independent of one another
P(system) = p(subcomp1 ∩ subcomp2)
P(system) = 1.60 x 0.64
P(system) = 1.0240
