Consider the system of components connected as in the accomp

Consider the system of components connected as in the accompanying picture below. Components 1 and 2 are connected in parallel, so that subsystem works iff either 1 or 2 works; since 3 and 4 are connected in series, that subsystem works iff both 3 and 4 work. If components work independently of one another and P(component works) = 0.8, calculate P(system works).

Solution

P(A1)=P(A2)=P(A3)=P(A4)=0.8

The system will work if 1 or 2 works, or 1 and 2 work, or 3 and 4 work, or 1 or 2 and 3 and 4 work, or if all four elements work. That