A foreman for an injection-molding firm admits that on 52% of his shifts, he forgets to shut off the injection machine on his line. This causes the machineto overheat, increasing the probability that a defective molding will be produced during the early morning run from 4% to 22%. The plant managerrandomly selects a molding from the early morning run and discovers it is defective. What is the probability that the foreman forgot to shut off themachine the previous night?Probability =

Let us define some events A : the forman forget to shut off the machine. B : the forman does not…

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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A blood bank asserts that a person with type O blood and a negative Rh factor (Rh−) can donate blood to any person with any blood type. Their data show that 49% of people have type O blood and 17% of people have Rh− factor; 52% of people have type O or Rh− factor. A. Find the probability that a person has both type O blood and the Rh− factor. B. Find the probability that a person does NOT have both type O blood and the Rh− factor.
When functioning correctly, a machine produces switches with a 0.8% defective rate. Find the probability that a batch of 1,000 switches contains 14 or more defective switches (assuming that the machine functions correctly, i.e., the population defective rate is 0.8%). Suppose a batch of 1,000 switches were inspected when completed, and 14 defective switches were found. Based on your answer to part a, does this sample imply that the machine needs adjustment? Explain your answer.
A new medical test has been designed to detect the presence of a certain disease. Among those who have the disease, the probability that the disease will be detected by the new test is 0.74. However, the probability that the test will erroneously indicate the presence of the disease in those who do not actually have it is 0.04. It is estimated that 14 % of the population who take this test have the disease.If the test administered to an individual is positive, what is the probability that the person actually has the disease?
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] =
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.
Question 2: You are appointed as a quality engineer in a telecommunication company. Your manager asks you to enhance the company quality of service, by increasing the success rate for customers to get hold of tech support representatives. Assume that customers will call three times is an attempt to ask for tech support then give up. You want to make sure that you are able to serve at least 97% of the people who ask for tech support. Let p be the probability that a caller get hold of a tech support representative. What is the minimum value of p necessary to meet your goal?
Question 9 A batch of 400 LEDS contains 7 that are defective. This is known to be the long-term average for the production. The company sells boxes with 50 LEDS in each box. (a) What is the probability there are 1 or more defective bulbs in a box? (b) If three LEDS are selected at random from a box, what is the probability that the third one selected is defective given that the first one selected was not defective and the second one selected was defective? (c) Boxes are returned if 3 or more are defective. What is the probably a box will be returned?
In a new fiber-optic communication system, trans- mission errors occur at the rate of 1.5 per twenty seconds. What is the probability that more than five errors will occur during the next minute?
Question 6 Company records show that the proportion of defective parts has historically been 5%, however a quality control engineer believes that due to budget cuts these numbers have increased. To test this claim a random sample of N = 15 parts will be taken and if more than two defective parts are found the inspector will conclude that the proportion of defective parts has increases. Calculate the probability of the type one error. 18.5% 81.5% О 3.6% O 96.4%
A Beneficiation Engineer is in charge of a particular process (crushing of ore at least 9-inch diameter) at a mining company. Past experience indicates that 10% of all shutdowns are due to equipment failure alone, 5% are due to a combination of equipment failure and operator error, and 40% involve operator error. A shutdown occurs. Find the probability that the operator error is involved given the equipment failure occurs.
QUESTION 3 At a particular garage 20% of the cars that arrive for repair have engine trouble. Upon arrival at the garage an engine diagnostic test is carried out on the car, but this engine diagnostic test is far from perfect. If the car has engine trouble the diagnostic test will turn out positive with a probability of 0.9. If the car does not have engine trouble, the diagnostic test will turn out positive with a probability of 0.05. For each of the questions below explain your answer i.e. show your reasoning. Q 3(d) If 10 cars arrive to the garage on a particular day, what is the probability that: (i) (ii) none of the cars will have engine trouble. the first car with engine trouble that arrives to the garage that day will be the 4th car.
Question 26 Renee buys a bag of cookies that contains 5 chocolate chip cookies, 7 peanut butter cookies, 5 sugar cookies, and 5 oatmeal cookies. What is the probability that Renee reaches in the bag and randomly selects a chocolate chip cookie from the bag, eats it, then reaches back in the bag and randomly selects a sugar cookie? Round your answer to four decimal places.

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