An agricultural storage warehouse uses a metal building system as a lateral force resisting system (LFRS). The building columns are attached to a concrete foundation with anchor bolts. Failure of either the LFRS or the anchor bolts will result in failure of the building. Either or both may fail at the same time. The probability of the bolts failing is 0.003. If the bolts fail, the probability that the LFRS also fails is 0.35. The probability of bolts failing due to failure of the LFRS is 0.25. 1. What is the probability of the failure of the building during high winds? 2. What is the probability that either the LFRS or the bolts fail? 3. If the LFRS is damaged, what is the probability that it was caused by the bolts failing?

An agricultural storage warehouse uses a metal building system as a lateral force resisting system (LFRS). The building columns are attached to a concrete foundation with anchor bolts. Failure of either the LFRS or the anchor bolts will result in failure of the building. Either or both may fail at the same time. The probability of the bolts failing is 0.003. If the bolts fail, the probability that the LFRS also fails is 0.35. The probability of bolts failing due to failure of the LFRS is 0.25. 1. What is the probability of the failure of the building during high winds? 2. What is the probability that either the LFRS or the bolts fail? 3. If the LFRS is damaged, what is the probability that it was caused by the bolts failing?

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...

See similar textbooks

Similar questions

What is the expected value for the number of defective LCDs3 10 2) 0.1 3) 0.45 4) 0.5 5) 0.9 06) 1
To reduce laboratory costs, water samples from five public swimming pools are combined for one test for the presence of bacteria. Further testing is done only if the combined sample tests positive. Based on past results, there is a 0.004 probability of finding bacteria in a public swimming area. Find the probability that a combined sample from five public swimming areas will reveal the presence of bacteria. Is the probability low enough so that further testing of the individual samples is rarely necessary? The probability of a positive test result is (Round to three decimal places as needed.)
The probability of a positive reaction of the patient to a test developed against a disease is 0.4. Calculate the probability that the first positive response will occur in experiment 5.
A blood bank asserts that a person with type O blood and a negative Rh factor (Rh−) can donate blood to any person with any blood type. Their data show that 49% of people have type O blood and 17% of people have Rh− factor; 52% of people have type O or Rh− factor. A. Find the probability that a person has both type O blood and the Rh− factor. B. Find the probability that a person does NOT have both type O blood and the Rh− factor.
The principle of redundancy is used when system reliability is improved through redundant or backup components. Assume that a student's alarm clock has a 16.5% daily failure rate. a. What is the probability that the student's alarm clock will not work on the morning of an important final exam? (Round to three decimal places as needed.) b. If the student has two such alarm clocks, what is the probability that they both fail on the morning of an important final exam? (Round to five decimal places as needed.) c. What is the probability of not being awakened if the student uses three independent alarm clocks? (Round to five decimal places as needed.)
Assume the chances of failure of each component is given in Figure. What is the probability that the system would not work? .
A rapid HIV test that gives results while a client at a clinic waits is unfortunately less accurate than slower lab tests.Applied to people who have no HIV antibodies,one rapid test has probability about 0.004 of producing a false positive.if a clinic tests 200 people who are free of HIV antibodies,what is the chance that at least one force positive will occur?
Engineers working for an aerospace company are designing coatings for the heat shielding tiles used to line the cone of a rocket. The tiles themselves are heat resistant, but they must be replaced after each launch. To prolong their lifespan, the engineers are applying two different heat-resistant coatings. If the coatings work, the tiles can be reused after each launch. There is only a 0.10 probability that the outermost coating fails, and a 0.018 probability that the second layer will fail. Only if both of the coatings fail will the tiles need to be replaced. If both of the coatings are used, what is the probability that the tiles can be reused after each launch?
A Beneficiation Engineer is in charge of a particular process (crushing of ore at least 9-inch diameter) at a mining company. Past experience indicates that 10% of all shutdowns are due to equipment failure alone, 5% are due to a combination of equipment failure and operator error, and 40% involve operator error. A shutdown occurs. Find the probability that the operator error is involved given the equipment failure occurs.