6. Machines A and B produce 40% and 60%, respectively of the production of a component intended for the electronics industry. From experience, it is known that the probability that machine A produces a defective component is 0.015 while the probability that machine B produces a defective component is 0.025. If a component is selected at random from a day's production, find the probability that the component is defective. If a component is selected at random from a day's production and is found to be defective, use Bayes' theorem to find the probability that it is made by machine A. а. b.

6. Machines A and B produce 40% and 60%, respectively of the production of a component intended for the electronics industry. From experience, it is known that the probability that machine A produces a defective component is 0.015 while the probability that machine B produces a defective component is 0.025. If a component is selected at random from a day's production, find the probability that the component is defective. If a component is selected at random from a day's production and is found to be defective, use Bayes' theorem to find the probability that it is made by machine A. а. b.

Name: 6. Machines A and B produce 40% and 60%, respectively of the producti
Uploaded: 2024-03-20T07:06:41.000Z
Channel: Bartleby
Description: 6. Machines A and B produce 40% and 60%, respectively of the production of a component intended for the electronics industry. From experience, itis known that the probability that machine A produces a defective component is 0.015 while the probabili

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Q: On average, 100 customers arrive per hour at Gotham City Bank. It takes a teller an average of two…

A: → Here arrival rate is λ=100 customerhour and service rate is μ=30customerhour…

Q: Suppose an insurance company has three types of customers-high risk, medium risk and low risk. From…

A: Given that: 25% of customers are high risk 25% of customers are medium risk 50% of customers are low…

Q: machine consists of two components: A and B. The machine needs both components to operate. As soon…

A: Given problem is:

Q: A data transmission channel malfunctions with probability 0.15, but it has a backup channel which…

A: A data transmission channel malfunctions with probability 0.15 but it has a backup channel which…

Q: Suppose that there are 19 sophomores and 22 juniors in a Physics class. Two students are chosen at…

A: 19 sophomores22 juniors ______________41 total studentsselect two students at randomP(first is…

Q: A stock index consists of businesses in both Europe and the United States. Assume that each business…

A: Given the probability that American business makes a profit = 90% = 0.90 Given the probability that…

Q: A doctor is seeking an anti-depressant for a newly diagnosed patient. Suppose that, of the available…

Q: minutes to serve a customer. Interarrival and service times are exponentially distributed. The bank…

Q: In a population of 10,000, there are 5000 nonsmokers, 2500 smokers of one pack or less per day, and…

A: Given Information: In a population of 10,000, there are 5000 smokers, 2500 smokers of one pack or…

Q: Example 2.19. Consider men who need to undergo a complicated surgery. The probability that they will…

A: In the given problem, the surgery is complicated as there is only 50% chance of survival for the…

Q: A doctor is seeking an anti-depressant for a newly diagnosed patient. Suppose that, of the available…

A: a. P[drug ineffective]= 1-P[drug effective]=1-0.36=0.64 Event that the patient will need to take 4…

Q: 1. A realistic estimate for the probability of an engine failure on a transatlantic flight is…

A: Given that, Let X be the random variable represents the number of an engine failure on a…

Q: Assume that a student's alarm clock has a9.4% daily failure rate. Complete parts (a) through (d)…

A: Given data: The principle of redundancy is used when system reliability is improved through…

Q: Assume the chances of failure of each component is given in Figure. What is the probability that the…

A: The probabilities that each of the component fails is mentioned. The probability that component A is…

Q: In a survey of U.S. adults with a sample size of 2097, 398 said Franklin Roosevelt was the best…

A: Note:Hi there! Thank you for posting the question. As the first three parts of the question are…

Q: (a) Find the probability that a failure is due to loose keys. (b) Find the probability that a…

Q: A store only sells two types of products: type A and type B. If a customer only buys product A, the…

Q: per day. For smokers who smoke a pack or less per day, there is a 10% probability of quitting and a…

Q: A smartphone manufacturer admits that 12% of the smartphones they make have defects that could…

A: 1. Given that X=the number of smartphones manufactured by this company that have defects that could…

Q: Power received at the radar receiver can be described in terms of an exponential random variable. In…

A: Power received when target is present is an exponential variable with mean of 16 mW.Power received…

Q: A machine consists of two components: A and B. The machine needs both components to operate. As soon…

A: The machine consists of two components A and B.

Q: Example 16 : If the probability that a communication system will have high fidelity is 0.81 and the…

Q: Is hoticed that the probability that the test detects an infected = 80%. Use Baeye's rule to…

A: Given probabilities are : P(system is infected)=0.60P(test detects an infected system)=0.90P(test…

Q: USA Today reported that approximately 25% of all state prison inmates released on parole become…

A: Given: x 0 1 2 3 4 5 P (x) 0.219 0.378 0.207 0.180 0.015 0.001

Q: Components of a certain type are shipped to a supplier in batches of 40. Suppose that 50% of all…

Q: a) Based on the information given above, write down what P(D), P(T|D) and P(T|D) are. Calculate P(D)…

Q: A factory has three machines such as A, B and C that produce 5 kΩ resistors. 80% of the resistors…

A: 1. A resistor produced by this factory will either be from machine A, B and C. Let E be the event…

Q: Based on a poll, among adults who regret getting tattoos, 17% say that they were too young when…

A: Let X is the random variable representing the number of adults who regret getting tattoos. Given:…

Q: A component of a spacecraft has both a main system and a backup system operating throughout a…

A: Given: A component of a spacecraft has both the main system and a backup system operating throughout…

Q: A student will take two trainee selection exams for companies A and B, respectively. He estimates…

A: Solution: Let A be the event that a student passing company A’s exam and B be the event that a…

Q: A stock index consists of businesses in both Europe and the United States. Assume that each business…

A: From the given information we make a table: Number of business 840 720 probability 60%=0.60…

Q: The principle of redundancy is used when system reliability is improved through redundant or backup…

A: given data P(students alarm clock will fail) = p = 0.165

Q: Assume the chances of failure of each component is given in Figure. What is the probability that the…

A: The system would work when A and D work and atleast 1 of B or C works Probability that the system…

Concept explainers

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.

Topic Video

Question

6. Machines A and B produce 40% and 60%, respectively of the production of a component intended for the electronics industry. From experience, it
is known that the probability that machine A produces a defective component is 0.015 while the probability that machine B produces a defective
component is 0.025.
If a component is selected at random from a day's production, find the probability that the component is defective.
а.
b.
If a component is selected at random from a day's production and is found to be defective, use Bayes' theorem to find the probability that it
is made by machine A.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 1 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Discrete Probability Distributions$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.

Similar questions

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?
In the basic science unit of the university, the following results were obtained from 350 students: 200 students passed the differential calculus course 160 passed physics course 187 passed probability-statistics course 112 approved differential calculus and probability-statistics 120 passed differential calculus and physics 95 passed physics and probability-statistics 80 passed the three courses. What is the probability of those who passed only one course? a. 0.051 b. 0.1714 c. 0.38 d. 0.0714
In a population of 10,000, there are 5000 nonsmokers, 2500 smokers of one pack or less per day, and 2500 smokers of more than one pack per day. During any month, there is a 5% probability that a nonsmoker will begin smoking a pack or less per day, and a 4% probability that a nonsmoker will begin smoking more than a pack per day. For smokers who smoke a pack or less per day, there is a 10% probability of quitting and a 10% probability of increasing to more than a pack per day. For smokers who smoke more than a pack per day, there is a 9% probability of quitting and a 10% probability of dropping to a pack or less per day. How many people will be in each group in 1 month, in 2 months, and in 1 year? (Round your answers to the nearest whole number.)(a) in 1 month:nonsmokers:1 pack/day or less:more than 1 pack/day:(b) in 2 months:nonsmokers:1 pack/day or less:more than 1 pack/day:(c) in 1 year:nonsmokers:1 pack/day or less:more than 1 pack/day:
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?
The Business School at State University currently has three parking lots, each containing 155 spaces. Two hundred faculty members have been assigned to each lot. On a peak day, an average of 70% of all lot 1 parking sticker holders show up, an average of 72% of all lot 2 parking sticker holders show up, and an average of 74% of all lot 3 parking sticker holders show up. a. Given the current situation, estimate the probability that on a peak day, at least one faculty member with a sticker will be unable to find a spot. Assume that the number who show up at each lot is independent of the number who show up at the other two lots. Compare two situations: (1) each person can park only in the lot assigned to him or her, and (2) each person can park in any of the lots (pooling). (Hint: Use the RISKBINOMIAL function.) If needed, round your answer to a whole percentage and if your answer is zero, enter "0". No pooling: Pooling: 51.4 % 83.8 % b. Now suppose the numbers of people who show up at…
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?
An investor is monitoring stocks from CompanyA and Company B, which each either increase or decrease each day. On a given day, suppose that there is a probability of 0.38 that both stocks will increase in price, and a probability of 0.11 that both stocks will decrease in price. Also, there is a probability of 0.16 that the stock from Company A will decrease while the stock from Company B will increase. What is the probability that the stock from Company A will increase while the stock from Company B will decrease? What is the probability that at least one company will have an increase in the stock price?
Do question 2
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.
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.)
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?