Consider the system of components in the accompanying picture. Components 3 and

Question

Consider the system of components in the accompanying picture. Components 3 and 4 are connected in series (call this subsystem 3-4). Subsystem 3-4 will work only if both components 3 and 4 work. In order for the entire system to function, it must be the case that component 1 functions (A_1) or component 2 functions (A_2) or that subsystem 3-4 functions (A_34). Suppose that each individual component functions independently of all other components and each component functions with probability 0.7. Find the probability that the entire system functions or P (A_1 u A_2 u A_34).

Explanation / Answer

ans=

P(link 1-2 fails) = 0.3*0.3 = 0.09

P(both 3 & 4 work) = 0.7*0.7 = 0.49
so P(link 3-4 fails) = 1 - 0.49 = 0.51

P(both link 1-2 & link fail) = 0.09*0.51 = 0.0459
thus P(system works) = 1 - 0.0459 = 0.9541

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