A foreman for an injection-molding firm admits that on 20% of his shifts, he forgetsto shut off the injection machine on his line. This causes the machine to overheat,increasing the probability that a defective molding will be produced during the earlymorning run from 2% to 20%. The plant manager randomly selects a molding fromthe early morning run and discovers it is defective. What is the probability that theforeman forgot to shut off the machine the previous night?Probability =

Answered: Image /qna-images/answer/171eeae7-24e9-46df-9caf-33ccdb8cff85.jpg

Answered: A foreman for an injection-molding firm…

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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Deer ticks can carry both Lyme disease and human granulocytic ehrlichiosis (HGE). In a study of ticks in the Midwest, it was found that 15 % carried Lyme disease, while 11 % carried HGE. In addition, of the ticks with either Lyme disease or HGE, 16 % carried both diseases. (a) What is the probability P[L H] that a tick carrries both Lyme disease (L) and HGE (H)? P[LH] = (b) What is the conditional probability that a tick carries HGE, given that it has Lyme disease? P[H|L] =
An investigative bureau uses a laboratory method to match the lead in a bullet found at a crime scene with unexpended lead cartridges found in the possession of a suspect. The value of this evidence depends on the chance of a false positive-that is, the probability that the bureau finds a match, given that the lead at the crime scene and the lead in the possession of the suspect are actually from two different "melts," or sources. To estimate the false positive rate, the bureau collected 1,809 bullets that the agency was confident all came from different melts. Then, using its established criteria, the bureau examined every possible pair of bullets and found 606 matches. Use this information to compute the chance of a false positive. Is this probability small enough for you to have confidence in the agency's forensic evidence? Choose the correct answer below and fill in the answer box to complete your choice. (Round to four decimal places as needed.) O A. The chance of a false positive…
To study the hormonal regulation of a metabolic line, albino rats are injected with a drug that inhibits the synthesis of proteins in the organism. In general, 8 out of 30 rats die from the drug before the experiment is over. If 10 animals are treated with the drug. What is the probability that 4 or fewer arrive alive at the end of the experiment? What is the probability that more than 8 will arrive alive at the end of the experiment? Note: Answer with at least 4 decimal places
Samuel F.B. Morse (1791 – 1872), the creator of Morse Code, claimed that 12% of all letters used in the English language were “e”s. Suppose random samples of 196 letters are selected from a book What is the probability that a random sample of 196 letters will contain at least 10% "e"s? Type your calculated z-score here. Express its value to the nearest hundredth (two decimal places). Type your probability here. Express its value to four decimal places. Do not round.
A state government hired a contractor for a road-construction project. The contractor's type, its cost efficienciency, is unknown to the government. There is 2/3 probability of the its construction cost being 3 (billion dollars per lane) and 1/3 probability of the cost being 5. More lanes yield more social benefit in the form of faster travel and fewer accidents. The social value V (measured in billions of dollars) from having N lanes on the highway is: V-15N-N?/2. The government is interested in choose N and writing a contract to maximize the benefit to the state (V) net of the fee paid to the contractor (call it F); G-V-F. Your goal as a government official is to design a pair of contracts to separate the types of contractor. You want the contractor to choose "Contract L: Build N lanes and get paid RL dollars" if its cost type is low cost of $3 (billion dollars per lane) and to choose "Contract H: Build NH lanes and get paid RH dollars" if its cost type is high cost $5 (billion…
Question 2 (a) One of the famous fast-food chains in Malaysia has a brand name recognition rate of 95% around the world. If we randomly select 16 people, (i) compute the probability that exactly 13 people recognize the brand. (ii) compute the probability that between 5 and 12 people do not recognize the brand.
Suppose that we have test for lung cancer, which correctly identifies those with the cancer 70 % of the time, and mistakenly identifies those without the cancer 5 % of the time. In the cohort of interest, the rate of this cancer is somewhat low: 0.9 %. Find the probability -- a number between 0 and 1 -- that someone diagnosed (testing positive) with this test actually has lung cancer.
A blockchain-based business received consensus validation via two different systems A and B. The time between validations for each validation system in a typical day is known to be exponentially distributed with a mean of 3.2 seconds. Both systems operate independently. Given the above distribution, the probability that no validation will be received from system A in a 5-second period is (expressed your answer in 4 decimal places). Likewise, the probability that no validation will be received from both systems in a 5-second period is (expressed your answer in 4 decimal places). If X denotes the number of validations in a 5-second interval. Then, X is a Poisson random variable with the lambda is equal to (expressed your answer in 4 decimal places). Then, the probability that both systems receive two validations between 10 and 15 seconds after the site is (expressed in 4 decimal places). officially open for business is
An antique collecter has been following the price of a certain old camera and he found out that the camera's price changes each day and it can either rise or fall in value. The price changes per day are assumed to be independent events. After observing the price for 8 months, he found out that the price rose for 40% of the days and it sunk for the rest. He wants to determine the probability that the camera will be a certain value on a particular day so he asked you for help. 1) What distribution does this problem follow? (Geometric, Binomial, Poission?) 2) Determine the probability that 7 days from now, the cost of the camera will be the same as it is today.3) Determine the probability that the camera's cost has increased from its current value after 5 days.
The probability of a randomly selected adult in one country being infected with a certain virus is 0.005. In tests for the virus, blood samples from 14 people are combined. What is the probability that the combined sample tests positive for the virus? Is it unlikely for such a combined sample to test positive? Note that the combined sample tests positive if at least one person has the virus. The probability that the combined sample will test positive is (Round to three decimal places as needed.) Is it unlikely for such a combined sample to test positive? O A. It is unlikely for such a combined sample to test positive, because the probability that the combined sample will test positive is less than or equal to 0.05. O B. It is not unlikely for such a combined sample to test positive, because the probability that the combined sample will test positive is less than or equal to 0.05. OC. It is not unlikely for such a combined sample to test positive, because the probability that the…

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