In automotive repair, experience has shown that a rough - running engine canbe attributed to the bad ignition wires 35% of the time, bad spark plugs 80%of the time, and both problems 20% of the time. Suppose a mechanic beginsto diagnose the problem by checking the spark plugs first and find them to bebad. Given this information, what is the probability that the wires are also bad?

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Answered: In automotive repair, experience has…

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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One of the reasons why the concept of an unfair coin is important in probability is that many real-life experiments can be modeled by a toss of an unfair coin. For example, if the probability of Laverne getting a hit when at bat is 0.36, then batting can be modeled by a toss of an unfair coin for which Heads is associated with Hitting and Tails with Missing. Thus, the probability of Laverne getting 3 hits out of 6 batting attempts is exactly the same as the probability of getting 3 heads from tossing the coin 6 times and can be computed using the following formula P(kH/n) = Cp*(1-p)"-k with n=6, k = 3, and p = 0.36: P(3H/6)=C-0.36³-0.64³20-0.046656 -0.262144 = 0.2446 Find the probability of Laverne getting 2 hits out of 9 batting attempts: (Round the answer to 4 decimal places.)
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?
Answer part a and b
Your car is making a funny noise. You believe that the problem is either with the wheel or the axle, and you believe the probability is 0.3 that the wheel needs to be replaced, and 0.7 that the axle needs to be replaced. You need to decide whether to replace the wheel or the axle first. The cost of each alternative is given in the following table (if you decided to replace the wrong part first, you have to replace both of them). The Wheel is broken p = 0.3 The Axle is broken p = 0.7 Replace Wheel First Replace Axle First 600 1500 1500 900 a) Find the EV of each decision alternative. Which part should you replace first? b) What is the EVPI?
The weather in a particular town in the Pacific northwest is classified as either good, indifferent or bad. If the weather is good on a particular day, the probability it will remain good the next day is only 11%, and there is a 45% chance it will be indifferent. If the weather is indifferent on a particular day, there is a 20% chance it will become good, and a 42% chance it will become bad. If the weather is bad on a particular day, there is a 48% chance it will be bad the next day, and a 21% chance it will become indifferent. Construct the stochastic matrix that models this problem.
June is a student taking a statistics course. Unfortunately, June is not a diligent student. She does not read the textbook before or after class, does not do homework, and regularly misses class. She intends to rely on luck to pass the next quiz. The quiz consists of 10 multiple-choice question. Each question has five possible answers. Only one of the answers is correct, so the probability of choosing the correct answer is 0.20. June plans to guess the answer to each question independently. Let � be the number of correct answers on June’s quiz. What is the standard deviation of correct answers for June? Group of answer choices 8 2 1.26 1.14 None of These
Can you do problem 6.58?
Analysts expects that 11% of all publicly traded companies will experience a decline in earnings next year. If a company is headed for a decline, there is a 74% chance that this ratio will be negative. If the company is not headed for a decline, there is only a 20% chance that the ratio will be negative. The analyst randomly selects a company and its ratio is negative. What is the probability that the company will experience a decline?
Problem (2): TV or a DVR? A consumer electronics company has observed that 36% of their customers purchased an LED screen television, 26% of their customers purchases a DVR, and 12 percent of their customers purchased both an LED screen TV and a DVR. Find the probability that a randomly chosen customer either purchases a plasma screen TV or a DVR.
A pharmaceutical company is running trials on a new test for anabolic steroids. The company uses the test on 400 athletes known to be using steroids and 200 athletes known not to be using steroids. Of those using steroids, the new test is positive for 375 and negative for 25. Of those not using steroids, the test is positive for 25 and negative for 175. What is the relative frequency of a false negative result (the probability that an athlete using steroids will test negative)? (Round your answer to two decimal places.) What is the relative frequency of a false positive result (the probability that an athlete not using steroids will test positive)? (Round your answer to two decimal places.)
You are a physician meeting with a patient who has just been diagnosed withcancer. You know there are two mutually exclusive types of cancer that the patientcould have: type A and type B. The probability that she has type A cancer is 1/3. TypeA is deadly: four patients out of five diagnosed with type A cancer die within one year.Type B is less dangerous: only one patient out of five diagnosed with type B cancerdies within one year. What is the probability that your patient has type A cancer and suc-cessfully survives it? What is the probability that your patient dies within a year? Suppose that your patient dies in less than one year before you learn the exact type of cancer he has. Given this sad happening, what is the probabilitythat she had type A cancer? (Hint: You want to start off by considering this question: given the informationprovided in the story (what those numbers are really about?), which of the twoanalytical tools we have covered in class will be more helpful to solve…
Thank you. I'm not sure about the result for the second question. What I'm having a hard time with is the probability that a total of 30 of the 546 crashes have occurred in the 48 time windows. My data shows that crashes occurred in 25 of these 48 time windows, with 3 in one of these and 2 in three others.

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