A certain type of car model has a defective part in its engine, causing the engine to fail10% of the time. However, the engine fails 2% of the time due to reasons other thanthe defective part. A dealership sells this car model and 0.5% of the cars sold have thedefective part.(a) What is the probability that a randomly selected car from the dealership will havean engine failure?(b) Calculate the conditional probability that a car selected at random from thedealership has the defective part, given that the engine has failed.

Let A denote the event that engine fails and B denote the event that the engine has defective part.…

Answered: A certain type of car model has a…

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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Does crime pay? The FBI Standard Survey of Crimes showed that for about 80% of all property crimes (burglary, larceny, car theft, etc.), the criminals are never found and the case is never solvedt. Suppose a neighborhood district in a large city suffers repeated property crimes, not always perpetrated by the same criminals. The police are investigating twelve property crime cases in this district. In USE SALT (a) What is the probability that none of the crimes will ever be solved? (Round your answer to three decimal places.) (b) What is the probability that at least one crime will be solved? (Round your answer to three decimal places.) (c) What is the expected number of crimes that will be solved? crimes What is the standard deviation? (Round your answer to two decimal places.) crimes (d) What is the smallest number of property crimes n that the police must investigate before they can be at least 90% sure of solving one or more cases? n = crimes
A biomedical research company produces 40% of its insulin at a plant in Kansas City, and the remainder is produced at a plant in Jefferson City. Quality control has shown that 0.75% of the insulin produced at the plant in Kansas City is defective, while 0.5% of the insulin produced at the plant in Jefferson City is defective. What is the probability that a randomly chosen unit of insulin came from the plant in Jefferson City given that it is defective?
A study found that 35% of the assisted reproductive technology (ART) cycles resulted in pregnancies. Twenty-two percent of the ART pregnancies resulted in multiple births. (a) Find the probability that a random selected ART cycle resulted in a pregnancy and produced a multiple birth. (b) Find the probability that a randomly selected ART cycle that resulted in a pregnancy did not produce a multiple birth. (c) Would it be unusual for a randomly selected ART cycle to result in a pregnancy and produce a multiple birth? Explain.
A test to determine whether a certain antibody is present is 99.2% effective. This means that the test will accurately come back negative if the antibody is not present (in the test subject) 99.2% of the time. The probability of a test coming back positive when the antibody is not present (a false positive) is 0.008. Suppose the test is given to six randomly selected people who do not have the antibody. (a) What is the probability that the test comes back negative for all six people? (b) What is the probability that the test comes back positive for at least one of the six people?
A School of Public Health completed a study on alcohol consumption on college campuses. They concluded that 21.5% of women attending all-women colleges abstained from alcohol, compared to 17.3% of women attending coeducational colleges. Approximately 5.5% of women college students attend all-women schools. Complete parts (a) and (b) below. (a) What is the probability that a randomly selected female student abstains from alcohol? The probability is nothing. (Type an integer or a decimal rounded to four decimal places as needed.)
The rates of on-time flights for commercial jets are continuously tracked by the U.S. Department of Transportation. Recently, Southwest Air had the best rate with 80 % of its flights arriving on time. A test is conducted by randomly selecting 15 Southwest flights and observing whether they arrive on time. (a) Find the probability that at least 4 flights arrive on time. (b) Would it be unusual for Southwest to have 3 flights arrive late?(Enter YES or NO)
A manufacturer of aspirin claims that the proportion of headache sufferers who get relief with just two aspirins is 63.5%. What is the probability that in a random sample of 480 headache sufferers, less than 59.4% obtain relief?
A manufacturing company regularly conducts quality control checks at specified periods on the products it manufactures. Historically, the failure rate for LED light bulbs that the company manufactures is 2%. Suppose a random sample of10 LED light bulbs is selected. Complete parts (a) through (d) below. (A) What is the probability that none of the LED light bulbs are defective? (B)What is the probability that exactly one of the LED light bulbs is defective? (C)What is the probability that three or fewer of the LED light bulbs are defective (D) What is the probability that four or more of the LED light bulbs are defective?
In a survey, 45% of the interviewees are of age below 30, 30% are between 30 and 50, and 25% are above 50. 90% of the interviewees aged below 30, 60% of the interviewees aged between 30 and 50, and 70% of the interviewees aged above 50 can swim. (a) If a randomly selected interviewee can swim, find the probability that his/her age is between 30 and 50. (b) If a randomly selected interviewee cannot swim, find the probability that his/her age is below 30.
A boy uses a homemade metal detector to look for valuable metal objects on a beach. The machine isn't perfect-it identifies only 98% of the metal objects over which it passes, and it identifies 4% of the nonmetallic objects over which it passes. Suppose that 25% of the objects that the machine passes over are metal. Find the probability that the boy has found a metal object when he receives a signal from the machine. Show your work.
A manufacturer of aspirin claims that the proportion of headache sufferers who get relief with just two aspirins is 62%. What is the probability that in a random sample of 560 headache sufferers, less than 59% obtain relief?
3.7% of a population are infected with a certain disease. There is a test for the disease, however the test is not completely accurate. 90.2% of those who have the disease test positive. However, 3.9% of those who do not have the disease also test positive (false positives). A person is randomly selected and tested for the disease. What is the probability that the person has the disease given that the test result is positive?

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