SITUATION 4The damage in a structure after an earthquake can be classified as either none, light, or heavy. For a newundamaged structure, the probabilities that it will suffer light and heavy damages after an earthquake are 20%and 5%, respectively. However, for an old structure with light damage from a previous earthquake, itsprobability of getting heavy damage during the next earthquake is 50%.(a) For a new structure, what is the probability that it will be heavily damaged after two earthquakes? Assumeno repairs were done after the first earthquake.(b) If the structure is heavily damaged after two earthquakes, what is the probability that the structure waseither undamaged or with light damage before the second earthquake?

Answered: Image /qna-images/answer/11b244ab-943b-491e-b109-a6f67d0ab067.jpg

Answered: SITUATION 4 The damage in a structure…

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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A jet fighter consists of two engines. The probability that the second engine functions in a satisfactory manner during its design life is 0.96, and the probability that at least one if the two engines does so is 0.98 and the probability that both engine do so is 0.935. Given that the first engine functions in a satisfactory manner throughout its design life, what is the probability that the second one also?
A jet fighter consists of two engines. The probability that the second engine functions in a satisfactory manner during its design life is 0.97, and the probability that at least one if the two engines does so is 0.975 and the probability that both engine do so is 0.93. Given that the first engine functions in a satisfactory manner throughout its design life, what is the probability that the second one also?
A manufacturing process produces, on the average, 3% defective items. The company ships 15 items in each box and wishes to guarantee no more than 1 defective item per box. If this guarantee accompanies each box, what is the probability that the box will fail to satisfy the guarantee?
Two machines turn out all the paper bags produced in the plant. Machine A produces 38% of the bags and machine B produces 62% of the bags. Machine A produces defective bags 1.9% of the time and machine B produces defective bags 3.8% of the time. Given a defective bag, what is the probability that it came from machine B?
Problem (2): TV or a DVR? A consumer electronics company has observed that 36% of their customers purchased an LED screen television, 26% of their customers purchases a DVR, and 12 percent of their customers purchased both an LED screen TV and a DVR. Find the probability that a randomly chosen customer either purchases a plasma screen TV or a DVR.
In 2013, the total sales from 3 different car production companies was 606,334 cars or light trucks. The probability that the vehicle was made by Company A was 0.381, by Company B 0.350, and by Company C 0.258. Additionally, the probability that a Company A vehicle sold was a car was 0.385, a Company B vehicle sold was a car was 0.370, and a Company C vehicle sold was a car was 0.332. Given the vehicle sold was a car, find the probability it was made by Company A. The probability a vehicle was made by Company A, given it was a car is (Round to three decimal places as needed.)
A doctor is seeking an anti-depressant for a newly diagnosed patient. Suppose that, of the available anti-depressant drugs, the probability that any particular drug will be effective for a particular patient is p = 0.32. What is the probability that the patient will need toa. take 4 different drugs until the effective one is found. b. take 5 different drugs until the effective one is found. c. take 7 different drugs until the effective one is found.
A gas station has three grades of fuel, regular, premium and diesel. Due to problems with the supply chain, the probabilities that the station will run out of any three fuel types in a week are 0.10, 0.16 and 0.24, respectively. These probabilities are statistically independent. Also, if there is a shortage of diesel, the probability of a shortage of premium becomes 0.25. 1. How likely is the station to run out of all three fuels in a given week? 2. What is the probability that if regular runs out, both premium and diesel will also run out? 3. What is the probability that the station will run out of at least one of either premium and diesel? 4. What is the probability that the station will run out of at least 2 of the fuels in a week?
If Johnny plays Russian Roulette twice, by spinning a revolver containing one bullet in one of the six chambers between each shot, what is the probability he doesn't shoot himself either time?
EXAMPLE 32. The probability that a contractor will get a plumbing contract is 2/3, and the probability that he will not get an electric contract is 5/9, the probability of getting at least one contract is 4/5, what is the probability that he will get both ?
A jet fighter consists of two engines. The probability that the second engine functions in a satisfactory manner during its design life is 0.96, and the probability that at least one if the two engines does so is 0.98 and the probability that both engine do so is 0.935. Given that the first engine functions in a satisfactory manner throughout its design life, what is the probability that the second one also?

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