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Consider the following system: → 0.71 → 0.71 → Determine the probability that the system will operate under each of these conditions: a. The system as shown. (Do not round your Intermedlate calculations. Round your final answer to 4 declmal places.) Probabllity b. Each system component has a backup with a probability of .71 and a switch that is 100% percent reliable. (Do not round your Intermedlate calculations. Round your final answer to 4 declmal places.) Probability c. Backups with 71 probablity and a switch that is 96 percent reliable. (Do not round your Intermedlate calculations. Round your final answer to 4 declmal places.) Probability

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Answer #1

a. Probability of system = R1*R2 = 0.71*0.71 = 0.5041 , (where R1 and R2 is the reliability of component 1 and 2 resp)

b. Probability of each component = 1 - probability that the component and back will fail simultaneously

= 1 - (1-0.71)^2 = 0.9159

Probability of system = 0.9159*0.9159 = 0.8389

c. Probability of each component with switch = 0.9159*0.96 = 0.8793

Probability of system = 0.8793*0.8793 = 0.7731

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