Consider the system of components connected as in the accompanying picture. Compo- nents 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. Sup- pose the components work independently of one another with probabilities p1, p2, p3, and p4:

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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Consider the system of components connected as in the accompanying picture. Compo-
nents 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. Sup-
pose the components work independently of one another with probabilities p1, p2, p3,
and p4:
(a) Find the probability that the system works in terms of p1, p2, p3, and p4.
(b) Calculate this probability for p1 = p2 = .9 and p3 = p4 = .8

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