4. Consider the system of electrical circuit below. Probabilities on the compone

Question

4. Consider the system of electrical circuit below. Probabilities on the components are reliabilities and all components are independent. The probability that a single component works is 0.92.
Let S1 be the subsystem consists of 1, 2 and 3. If and only if at least one of components (1, 2 or 3) works the subsystem S1 works. If and only if both S1 and 4 work, the system works.   

a. What is the probability that the subsystem S1 works?

b. What is the probability that the system works? Use p to substitute the answer of part (a) if you cannot solve part (a).

Explanation / Answer

Let

1, 2, 3, 4 = the events where the respective components are working

a)

P(S1) = P(1 or 2 or 3) = P(1) + P(2) + P(3) - P(1)P(2) - P(2)P(3) - P(1)P(3) + P(1)P(2)P(3) = 0.92 + 0.92 + 0.92 - 0.92*0.92 - 0.92*0.92 - 0.92*0.92 + 0.92*0.92*0.92

P(S1) = 0.999488 [ANSWER]

***************

B)

P(S1 and 4) = P(S1) P(4) = 0.999488*0.92 = 0.91952896 [ANSWER]

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