Consider the system of components connected as in the following picture 4 Compon
ID: 3355152 • Letter: C
Question
Consider the system of components connected as in the following picture 4 Components 1 and 2 are connected in parallel, so that their subsystem works if either 1 or 2 works Components 3 and 4 are connected in series, so that their subsystem works only if both 3 and4 work. The two subsystems are connected in parallel, so the system will work if either subsystem works. The components work independently of one another and the probability that the component works is 0.9 for components 1 and 2 and 0.8 for components 3 and 4. What is the probability that the system works?Explanation / Answer
Answer to the question is as follows. Write back in case you have doubts:
The upper part works when either of them works
P(upper part works) = 1-P(upper part doesn't work) = 1-(1-.9)(1-.9) = .99
P(down part works) = P(both part work) = .8*.8 = .64
P(whole circuit works) = 1 - P(either doesn't work) = 1- (1-.99)*(1-.64) = 0.9964
The probability that the system works is 0.9964