My Notes Ask Your Teache 10. +-1 points Consider the system of components connec

Question

My Notes Ask Your Teache 10. +-1 points Consider the system of components connected as in the accompanying picture. Components 1 and 2 are connected in parallel, so that subsystem works if and only if either 1 or 2 works; since 3 and 4 are connected in series, that subsystem works if and only if both 3 and 4 work. If components work independent , of one another and P component works -o 0 i = 1, 2 and 0.67 for i = 3, 4, calculate P(system works). (Round your answer to four decimal places.) 4 Need Help? Readit Talk to a Tuter

Explanation / Answer

P( system works) = ?

= P( 1 or 2 works ) or P( 3 and 4 works)

So, 1 or 2 fails when both 1 and 2 fail,

So, P( 1 or 2 works) = 1-P( 1or 2 fails) = 1- P( both fail) = 1- (1-P(1 fails)*P(2 fails)) = 1- (1-.71)(1-.71) = .9159

P( 3 and 4 work ) = P( 3 works)*P(4 works) = .67*.67

P( system works) = P( 1 or 2 works ) or P( 3 and 4 works) = 1- P( upper and lower network fail)

= 1-(1-.9159)*(1- 0.67*0.67) = .9537

So, answer is 0.9537

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