In a plant with 3 machines A, B and C, the same product is manufactured. Machine A produces 55% of the total items, while 25% and 20% are produced by machines B and C, respectively. In addition, the average number of defective items produced by each of the machines is known: 2%, 1.5% and 3%. The general supervisor discovers two defective items ready to go on sale. a) What is the probability that a defective item was produced by each of the three machines? b) What is the probability that the two defective items were produced by each of the three machines? c) What is the most likely event: that the defective items have been produced by machine A; B; C; one for A, another for B; C?

In a plant with 3 machines A, B and C, the same product is manufactured. Machine A produces 55% of the total items, while 25% and 20% are produced by machines B and C, respectively. In addition, the average number of defective items produced by each of the machines is known: 2%, 1.5% and 3%. The general supervisor discovers two defective items ready to go on sale. a) What is the probability that a defective item was produced by each of the three machines? b) What is the probability that the two defective items were produced by each of the three machines? c) What is the most likely event: that the defective items have been produced by machine A; B; C; one for A, another for B; C?

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...

See similar textbooks

Similar questions

A study tracked a large group of people for 10 years. At the start of the study, 20% were heavy smokers (H), 30% were light smokers (L), and 50% were non-smokers (N). The interest of the study was whether the people in the study died during the study (D) or not die (Dc ). The probability that a light smoker died during the study was twice that of the probability of a non-smoker dying. Also, the probability that light smoker died during the study was half that of the probability of a heavy smoker dying. A randomly selected person from the study died during the study. What is the probability that this person was a heavy smoker (given they died, what is the probability they were a heavy smoker H)?
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:
In a game of blackjack played with one deck, a player is initially dealt 2 different cards from the 52 different cards in the deck. A winning blackjack hand is won by getting 1 of the 4 aces, and 1 of 16 other cards worth ten points The two cards can be in any order. Find the probability of being dealt a blackjack hand. What approximate percentage of hands are winning blackjack hands?
If you have a sample of 100 patients at a hospital and 20 of them have the flu, what is the probability Of randomly selecting 3 patients in a row who have the flue?
In 2013, the total sales from 3 different car production companies was 606,334 cars or light trucks. The probability that the vehicle was made by Company A was 0.386, by Company B 0.350, and by Company C 0.258. Additionally, the probability that a Company A vehicle sold was a car was 0.379, a Company B vehicle sold was a car was 0.370, and a Company C vehicle sold was a car was 0.332. Given the vehicle sold was a car, find the probability it was made by Company A. The probability a vehicle was made by Company A, given it was a car is (Round to three decimal places as needed.)
A pharmacist receives a shipment of 2121 bottles of a drug and has 44 of the bottles tested. If 66 of the 2121 bottles are contaminated, what is the probability that less than 33 of the tested bottles are contaminated?
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?
In 2013, the total sales from 3 different car production companies was 606,334 cars or light trucks. The probability that the vehicle was made by Company A was 0.381, by Company B 0.350, and by Company C 0.258. Additionally, the probability that a Company A vehicle sold was a car was 0.385, a Company B vehicle sold was a car was 0.370, and a Company C vehicle sold was a car was 0.332. Given the vehicle sold was a car, find the probability it was made by Company A. The probability a vehicle was made by Company A, given it was a car is (Round to three decimal places as needed.)
If 3 % of the electric bulbs manufactures by a company are defective, find the probability that in a sample of 100 bulbs: a. 0 bulbs will be defective b. 1 bulbs will be defective c. 2 bulbs will be defective d. 3 bulbs will be defective e. 5 bulbs will be defective
In the last week of the semester, Stéphane decides to “reward” the students by no longer limiting himself to 4 exercises and instead assigning every activity he writes. If a student with a 60% chance of correctly answering an exercise is expected to answer three correctly, what is the probability that Stéphane did not have a visitor that week?