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A certain system is based on two indeperndent modules, A and B. A failure of any one of these modules causes a failre of the whole system. The lifetime of cach module has Exponential distribution with the following parameters. Modules A's lifetime. A - 0.100 years Modules B's lifetime: A = 0.250 years a. What is the probability that the system works at least 12 years without a failure? b. Given that the system failed during the first 12 years, what is the probability that it failed due to the failure of component 8 (but not component A)? Write your answers by providing 3 digits after the decimal point.

A certain system is based on two indeperndent modules, A and B. A failure of any one of these modules causes a failre of the whole system. The lifetime of cach module has Exponential distribution with the following parameters. Modules A's lifetime. A - 0.100 years Modules B's lifetime: A = 0.250 years a. What is the probability that the system works at least 12 years without a failure? b. Given that the system failed during the first 12 years, what is the probability that it failed due to the failure of component 8 (but not component A)? Write your answers by providing 3 digits after the decimal point.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 32E
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A certain systerm is based on two independent modules, A and B. A failure of any one of these modules causes a failure of the whcle system. The lifetime of cach module has Exponential distribution with the folloing parameters. Modules A's lifetime A = 0.100 years Modules B's lifetime: A = 0.250 years a. What is the probability that the system works at least 12 years without a failure? b. Given that the system failed during the first 12 years, what is the probability that it failed due to the failure of component 8 (but not component A)? Write your answers by providing 3 digits after the decimal point.
Transcribed Image Text:A certain systerm is based on two independent modules, A and B. A failure of any one of these modules causes a failure of the whcle system. The lifetime of cach module has Exponential distribution with the folloing parameters. Modules A's lifetime A = 0.100 years Modules B's lifetime: A = 0.250 years a. What is the probability that the system works at least 12 years without a failure? b. Given that the system failed during the first 12 years, what is the probability that it failed due to the failure of component 8 (but not component A)? Write your answers by providing 3 digits after the decimal point.
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