Consider the system of components connected as in the accompanying picture. 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 $P(\text{component works})=.9$, calculate $P(\text{system works})$.

Remark: The exercise is copied from the reference book Devore2017B.