C A B D
Consider the system of components connected as depicted below. The system can be thought
of as being comprised of two subsystems: one with components A and B, and the other with
components C and D. Components A and B are connected in parallel, therefore that subsystem
works iff either A or B works. Since C and D are connected in series, that subsystem works iff
both C and D work. Components work independent of each other (that is, operation/failure of
one component doesn’t influence the operation/failure of
another). If
so on, then P(A) = 0.9, P(B) = 0.88, P(C) = 0.94, and
P(D) = 0.98.
a. Calculate P(system works) as a
P(∙) notation – no numbers.
b. Calculate the quantity for P(system works). That is,
plug component probabilities into part a and
calculate.
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