Consider the system on the schematic shown next Assume compo

Consider the system on the schematic shown next. Assume components 1–5 have a 10% failure rate, while components 6 and 7 have a 5% failure rate. Further assume that the failure of one component has no effect on the failure of another component. Let C_i to denote the event where component i operates, i = {1,2,...,7}.

What is the probability that the system does NOT operate?

Solution

for 1.2.3 ----------- 0.10*0.10*0.10 = 0.001

for 4,5 ---------0.10*0.10= 0.01

for 6-------------0.05

1,2,3 with 4,5 with 6 = 0.001+0.01+0.05 = 0.061

1,2,3 with 4,5 with 6 * 7 = 0.061*0.05 = 0.00305