E. Suppose that a local factory uses a type of equipment called a super-drill. Suppose that at the start ofeach day, the machine must be restarted. Suppose that upon restarting, there is a .95 probability thatthe machine boots into normal mode, and a .05 probability that the machine boots into problem mode,independent of all else. Suppose that if the machine is in normal mode, each hole drilled is highquality with probability .98, and low quality with probability.02, independently for each hole drilledthat day. Suppose that if the machine is in problem mode, each hole drilled is high quality withprobability .55, and low quality with probability .45, independently for each hole drilled that day.What is the probability that the first hole drilled tomorrow is of low quality?b. Suppose that you are told that the first hole drilled tomorrow is of high quality. What is theconditional probability that the drill is in normal mode that day?c. Suppose that you are told that tomorrow exactly 10 holes are drilled, and that at least 2 of theseholes are high quality. What is the conditional probability that the drill is in normal mode that.day?a.SW atunim ano

Answered: Image /qna-images/answer/2b682651-e5ae-45aa-86af-2ec3bba4612b.jpg

Answered: Suppose that a local factory uses a…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Suppose that the rats on the campus of Hypothetical U are found to be carriers of bubonic plague. Eradicating the rats has an estimated cost of $1,000,000 and is expected to reduce the probability a given student dies of the plague from 1/3,000 to zero. Suppose that there are 30,000 students on campus. Suppose further that the administration refuses to eradicate the rats due to the cost. From this information, we can estimate that the administration's willingness to pay to save a student statistical life is no more than $100,000 $1,000,000 $50,000 $33,333
Assume the chances of failure of each component is given in Figure. What is the probability that the system would not work? .
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 5.6% daily failure rate. Complete parts (a) through (d) below. a. What is the probability that the student's alarm clock will not work on the morning of an important final exam? 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? c. What is the probability of not being awakened if the student uses three independent alarm clocks? d. Do the second and third alarm clocks result in greatly improved reliability? A. No, because the malfunction of both is equally or more likely than the malfunction of one. B. No, because total malfunction would still not be unlikely. C. Yes, because total malfunction would not be impossible, but it would be unlikely. D. Yes, because you can always be certain that at…
From observations of the weather, it is known that on October 20 the probability of rain is 0.85. A certain forecast method for October 20 is correct 0.9 times if rain is predicted and 0.75 times if no rain is predicted. How much information does a real weather forecast provide 20 th of October?
In airline applications, failure of a component can result in catastrophe. As a result, many airline components utilize something called triple modular redundancy. This means that a critical component has two backup components that may be utilized should the initial component fail. Suppose a certain critical airline component has a probability of failure of 0.039 and the system that utilizes the component is part of a triple modular redundancy. (a) What is the probability that the system does not fail? (b) Engineers decide to the probability of failure is too high for this system. Use trial and error to determine the minimum number of components that should be included in the system to result in system that has greater than a 0.99999999 probability of not failing. (a) The probability is (Round to eight decimal places as needed.)
Your character, a level 1 fighter, attacks a goblin with a longsword. An attack will hit if your Attack Roll is equal to or exceeds the target's Armor Class (AC). You make an attack roll by rolling a d20 and adding your Ability Modifier (Strength in this case) and Proficiency Bonus. Suppose that you have a strength modifier of +3, a proficiency bonus of +2, and that the goblin's AC is 12. Calculate the probability that your attack will hit the goblin. Note: The ability modifier used for a melee weapon attack is Strength, and the ability modifier used for a ranged weapon attack is Dexterity. Weapons that have the finesse or thrown property break this rule.
Suppose that a local factory uses a type of equipment called a super-drill. Suppose that at the start of each day, the machine must be restarted. Suppose that upon restarting, there is a .95 probability that the machine boots into normal mode, and a .05 probability that the machine boots into problem mode, independent of all else. Suppose that if the machine is in normal mode, each hole drilled is high quality with probability .98, and low quality with probability .02, independently for each hole drilled that day. Suppose that if the machine is in problem mode, each hole drilled is high quality with probability .55, and low quality with probability .45, independently for each hole drilled that day. What is the probability that the first hole drilled tomorrow is of low quality? Suppose that you are told that the first hole drilled tomorrow is of high quality. What is the conditional probability that the drill is in normal mode that day? Suppose that you are told that tomorrow exactly 10…
From observations of the weather, it is known that on October 20 the probability of rain is 0.25. A certain forecast method for October 20 is correct 0.9 times if rain is predicted and 0.75 times if no rain is predicted. How much information does a real weather forecast provide 20 th of October?
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 =…
(b) Test two independent circuits one after the other. On each test, the possible outcome is either overvoltage (0) or undervoltage (U). Assume that all circuits are overvoltage with probability 0.4. Let X be the number of overvoltage circuit in the first test and Y be the number of overvoltage circuit before you observed undervoltage. If both circuit is overvoltage or undervoltage, Y = 2. Find the joint PMF of X and Y.
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.)
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?

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