Consider a system of components connected as shown in the following figure. Components 1 and 2 are connected in parallel, so that their subsystem functions correctly if either component 1 or 2 functions. Components 3 and 4 are connected in series, so their subsystem works only if both components work correctly. If all components work independently of one another and P(a given component works) = .9, calculate the probability that the entire system works correctly.

Fig: 1

Fig: 2

Fig: 3