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.
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
Related questions
Question
![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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7c211531-3014-4521-81b5-1cdb138105b3%2F92a4afab-da44-4e53-b889-ae1317741c80%2F6kh067k_processed.jpeg&w=3840&q=75)
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.
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 1 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, probability and related others by exploring similar questions and additional content below.Recommended textbooks for you
![A First Course in Probability (10th Edition)](https://www.bartleby.com/isbn_cover_images/9780134753119/9780134753119_smallCoverImage.gif)
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON
![A First Course in Probability](https://www.bartleby.com/isbn_cover_images/9780321794772/9780321794772_smallCoverImage.gif)
![A First Course in Probability (10th Edition)](https://www.bartleby.com/isbn_cover_images/9780134753119/9780134753119_smallCoverImage.gif)
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON
![A First Course in Probability](https://www.bartleby.com/isbn_cover_images/9780321794772/9780321794772_smallCoverImage.gif)