You're a quality control inspector at a brewery, where you inspect the beer canning process. There are three production lines that produce beer cans, and you identify nonconforming beer cans according to five defect types. The table below provides the proportions of defect types for nonconforming cans for each of the three lines during a particular time period. During this period, line 1 produced 500 nonconforming cans, line 2 produced 400 such cans, and line 3 produced 600 such cans. Suppose that one of these 1500 cans was selected randomly. a. What is the probability that the can was produce by line 1? b. What is the probability that the reason for the nonconformance is a surface defect? c. Given that the selected can had a surface defect, what is the probability that it came from line 3? Defect type Blemish Crack Pull-tab problem Surface defect Other Line 1 0.15 0.50 0.21 0.10 0.04 Line 2 0.12 0.44 0.28 0.08 0.08 Line 3 0.20 0.40 0.24 0.15 0.01

You're a quality control inspector at a brewery, where you inspect the beer canning process. There are three production lines that produce beer cans, and you identify nonconforming beer cans according to five defect types. The table below provides the proportions of defect types for nonconforming cans for each of the three lines during a particular time period. During this period, line 1 produced 500 nonconforming cans, line 2 produced 400 such cans, and line 3 produced 600 such cans. Suppose that one of these 1500 cans was selected randomly. a. What is the probability that the can was produce by line 1? b. What is the probability that the reason for the nonconformance is a surface defect? c. Given that the selected can had a surface defect, what is the probability that it came from line 3? Defect type Blemish Crack Pull-tab problem Surface defect Other Line 1 0.15 0.50 0.21 0.10 0.04 Line 2 0.12 0.44 0.28 0.08 0.08 Line 3 0.20 0.40 0.24 0.15 0.01

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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Anita's, a fast-food chain specializing in hot dogs and garlic fries, keeps track of the proportion of its customers who decide to eat in the restaurant (as opposed to ordering the food "to go"), so it can make decisions regarding the possible construction of in-store play areas, the attendance of its mascot Sammy at the franchise locations, and so on. Anita's reports that 45% of its customers order their food to go. If this proportion is correct, what is the probability that, in a random sample of 4 customers at Anita's, exactly 3 order their food to go? Round your response to at least three decimal places. (If necessary, consult a list of formulas.)
B. A manufacturing company is analyzing its accident record. The accidents fall into two categories: ➤Minor-dealt with by first aider: Average cost k50 Major-hospital required. Average cost k1,000 The company has 1,000 employees, of which 180 are office staff and the rest work in the factory. The analysis shows that 10% of employees have an accident each year and 20% of accidents are major. It is assumed that an employee has more than one accident in a year. (i) Determine the expected total cost of accidents in a year. On further analysis it is discovered that a member of office staff has half the probability of having an accident relative those in the factory. (ii) Show that the probability that a given a member of office staff has an accident in a year is 0.0549. (iii) Determine the probability that a randomly chosen employee who has had an accident is office staff.
B. A manufacturing company is analyzing its accident record. The accidents fall into two categories: ➤Minor-dealt with by first aider: Average cost k50 ➤ Major-hospital required. Average cost k1,000 The company has 1,000 employees, of which 180 are office staff and the rest work in the factory. The analysis shows that 10% of employees have an accident each year and 20% of accidents are major. It is assumed that an employee has more than one accident in a year. (i) Determine the expected total cost of accidents in a year. On further analysis it is discovered that a member of office staff | half the probability of having an accident relative those in the factory. (ii) Show that the probability that a given a member of office staff has an accident in a year is 0.0549. (iii) Determine the probability that a randomly chosen employee who has had an accident is office staff.
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