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Could you please help with part b?

Could you please help with part b?

A First Course in Probability (10th Edition)
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...
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Could you please help with part b?

**Problem 2.63: Settlement Problems of a Structure** The structure shown in the diagram could experience settlement problems. The likelihood of settlement (event A) is influenced by the subsoil conditions, specifically whether a weak zone is present or not. - **Event S:** Small weak zone with a probability of settlement (A) as 0.2. - **Event L:** Large weak zone with a probability of settlement (A) as 0.6. - **Event N:** No weak zone with a probability of settlement (A) as 0.05. Based on geological data and previous site exploration, engineers estimate: - A 70% chance of having no weak zone (event N). - If there is a weak zone, it’s twice as likely to be small than large. The figure shows a structure with an underlying weak zone, asking if it's large or small. **Questions and Answers:** (a) **Probability of Settlement Problem** - What is the probability that the structure will have a settlement problem? - **Answer:** 0.135 (b) **Additional Boring Analysis** If a new boring is conducted to assess weak material presence, engineers estimate: - 80% chance of encountering a large weak zone. - 30% chance for a small weak zone. - No weak zone results in no encounter. Assuming the boring finds no weak material, determine: i. **Probability of a Large Weak Zone** - **Answer:** 0.023 ii. **Probability of a Small Weak Zone** - **Answer:** 0.163 iii. **Probability of Settlement Problem Given No Weak Zone Found** - **Answer:** 0.087 This analysis helps assess risks associated with structural settlement due to weak subsoil conditions.
Transcribed Image Text:**Problem 2.63: Settlement Problems of a Structure** The structure shown in the diagram could experience settlement problems. The likelihood of settlement (event A) is influenced by the subsoil conditions, specifically whether a weak zone is present or not. - **Event S:** Small weak zone with a probability of settlement (A) as 0.2. - **Event L:** Large weak zone with a probability of settlement (A) as 0.6. - **Event N:** No weak zone with a probability of settlement (A) as 0.05. Based on geological data and previous site exploration, engineers estimate: - A 70% chance of having no weak zone (event N). - If there is a weak zone, it’s twice as likely to be small than large. The figure shows a structure with an underlying weak zone, asking if it's large or small. **Questions and Answers:** (a) **Probability of Settlement Problem** - What is the probability that the structure will have a settlement problem? - **Answer:** 0.135 (b) **Additional Boring Analysis** If a new boring is conducted to assess weak material presence, engineers estimate: - 80% chance of encountering a large weak zone. - 30% chance for a small weak zone. - No weak zone results in no encounter. Assuming the boring finds no weak material, determine: i. **Probability of a Large Weak Zone** - **Answer:** 0.023 ii. **Probability of a Small Weak Zone** - **Answer:** 0.163 iii. **Probability of Settlement Problem Given No Weak Zone Found** - **Answer:** 0.087 This analysis helps assess risks associated with structural settlement due to weak subsoil conditions.
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