A particular automatic sprinkler system has two different types of activation devices for each sprinkler head. One type has a reliability of 0.75; that is, the probability that it will activate the sprinkler when it should is 0.75. The other type, which operates independentlyof the first type, has a reliability of 0.85. If either device is triggered, the sprinkler will activate. Suppose a fire starts near a sprinkler head. (provide your answer in four decimal numbers)(i) What is the probability that the sprinkler head will be activated? (1.5)(ii) What is the probability that the sprinkler head will not be activated? (1.5)(iii) What is the probability that both activation devices will work properly? (1.5)(iv) What is the probability that only the device with reliability 0.75 will work properly? (1.5)

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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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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 manager at the local auto shop has found that the probability that a car brought into the shop requires an oil change is 0.65, the probability that a car brought into the shop requires brake repair is 0.35, and the probability that a car requires both an oil change and brake repair is 0.24. For a car brought into the shop, determine the probability that the car will require an oil change or brake repair. The probability that the car requires an oil change or brake repair is (Type an integer or a decimal.)
Both flu and covid produce fevers. You know from past research that 10% of the population gets flu each year, but it is possible to get both covid and flu. Assume that the probability of getting flu and covid are independent. If this year the percentage of people reporting fever is 20%, what percentage of the population has covid? Studies show that due to similar transmission of flu and covid, someone who has covid has a 20% chance of also getting flu. What then is the probability of someone who has flu also having covid? Given the conditional information above, what is a better estimate of the percentage of people who have covid given the 20% fever reporting?
On any given morning here at Chabot College, coffee is brewed in the Science and Math Division workroom by one of two faculty members, depending on who arrives first at work. Instructor Yest arrives first 75% of the time. Instructor Kelly arrives first the remaining mornings. The probability that the coffee is brewed strong when brewed by Instructor Yest is 0.2. The probability that the coffee is brewed strong when brewed by Instructor Kelly is 0.9, as Instructor Kelly likes her coffee strong! Given the coffee is strong on a randomly selected morning, what is the probability that is was brewed by Instructor Yest?
Suppose that on any given day, there is a 20% chance that Lebron has a bad day, a 50% day that Lebron has a so-so day, and a 30% chance that Lebron has a good day. On a bad day, the probability that Lebron makes any given 3-point shot is 0.5. On a so-so day, the probability that Lebron makes any given 3-point shot is 0.7. On a good day, the probability that Lebron makes any given 3-point shot is 0.9. Suppose that tomorrow, Lebron takes a 3-point shot, and we record whether he hits or misses and what kind of day he was having. What is the probability that Lebron hits? What is the probability that if Lebron is having a bad day given that he misses a shot that day?
Based on a study from the Chronicles of Flippin'' Awesomeness, the probability that Napoleon and Pedro make it to their first period class on time is 0.30. The probability that they make it to their first period class on time, given that they catch the bus is 0.90. The probability that Napoleon and Pedro catch the bus and make it to their first period class on time is 0.21. What is the probability that Napoleon and Pedro catch the bus?

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