PROBLEM 32 (pg 87, #80-see diagram below) Consider the system of components in t

Question

PROBLEM 32 (pg 87, #80-see diagram below) 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) or component 2 functions (A2) or that subsystem 3-4 functions (As4). Suppose that each individual component functions independently of all other components and each component functions with probability 0.6. Find the probability that the entire system functions or P(4 UA, UA) Hint: determine P(A34). It isn't 0.60. 2 3 4

Explanation / Answer

probability that system 1-2 works =1-P(none of 1 or 2 works) =1-(1-0.6)*(1-0.6)=0.84

probability that system 3-4 works =0.6*0.6 =0.36

hence probability that entire system functions =1-P( neither 12 works nor 34 works)

=1-(1-0.84)*(1-0.36)=0.8976

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