If a circuit contains four automatic switches and we want that, with a probability of 99%, during a given time interval the switches to be all working, what probability of failure per time interval can we admit for a single switch?
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If a circuit contains four automatic switches and we want that, with a
during a given time interval the switches to be all working, what probability of failure per time
interval can we admit for a single switch?
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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.)1. The basketball coach says that based on Noah's free throws this season, Noah has a 3/4 probability of making each free throw. Select all the ways Noah could accurately simulate the number of free throws he will make in his next 6 attempts. *Testing for a disease can be made more efficient by combining samples. If the samples from two people are combined and the mixture tests negative, then bothsamples are negative. On the other hand, one positive sample will always test positive, no matter how many negative samples it is mixed with. Assuming the probability of a single sample testing positive is 0.1,find the probability of a positive result for two samples combined into one mixture. Is the probability low enough so that further testing of the individual samples is rarely necessary? (Round to three decimal places as needed.) Is the probability low enough so that further testing of the individual samples is rarely necessary? A. The probability is low, so further testing will be necessary for all of the combined mixtures. B. The probability is low, so further testing of the individual samples will be a rarely necessary event. C. The probability is not low, so further…
- Assume the chances of failure of each component is given in Figure. What is the probability that the system would not work? .Suppose that each time Bar-bie throws a dart, she has a 3/4 probability of getting a bullseye. If Barbie shoots three darts, what is the probability that she gets a bullseye on at least two of them?On a certain stretch of the East Coast Expressway, on average three birds per week are killed colliding with passing vehicles. The highway authority decides that if the probability of more than three birds per week being hit is more than 0.1, a special committee will be appointed to deal with the problem. Q1 (a) Determine whether the special committee will be appointed or not.
- You are the teacher of two math classes of 20 and 25 students respectively. To get into a university program, the students need a 75% in the class. Suppose each student has a 0.7 probability of getting atleast a 75% in the class. Let X1 be the number of students in the class of 20 who receive atleast a 75%. Let X2 be the number of students in the class of 25 who receive atleast a 75%. a. Do X1 and X2 fit the binomial setting? Are there any issues? For the rest of the question, assume both X1 and X2 can be modeled by a binomial distri- bution. b. What is the probability that exactly 15 students in the class of 20 get into the pro- gram? Do not use Table C. c. What is the probability that atleast 22 students in the class of 25 get into the pro- gram? Do not use Table C. d. Using Table C, what is the probability that atleast 17 students in the class of 20 get into the program? е. Let X be the number of students in both classes that get into the program. Deter- mine the mean and standard…A major traffic problem in the Greater Cincinnati area involves traffic attempting to cross the Ohio River from Cincinnati to Kentucky using Interstate 75. Let us assume that the probability of no traffic delay in one period, given no traffic delay in the preceding period, is 0.95 and that the probability of finding a traffic delay in one period, given a delay in the preceding period, is 0.75. Traffic is classified as having either a delay or a no-delay state, and the period considered is 30 minutes. (a) Assume that you are a motorist entering the traffic system and receive a radio report of a traffic delay. What is the probability that for the next 60 minutes (two time periods) the system will be in the delay state? Note that this result is the probability of being in the delay state for two consecutive periods. = (b) What is the probability that in the long run the traffic will not be in the delay state? (Enter your probabilities as fractions.) No Traffic Delay Traffic Delay π 1 =…Testing for a disease can be made more efficient by combining samples. If the samples from six people are combined and the mixture tests negative, then all six samples are negative. On the other hand, one positive sample will always test positive, no matter how many negative samples it is mixed with. Assuming the probability of a single sample testing positive is 0.05, find the probability of a positive result for six samples combined into one mixture. 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.)
