Chris recommends her friend to her supervisor for a job. To make her recommendation credible, she can design a test for her friend to take. She can choose the difficulty level of the test by choosing the following two parameters: X = Pr(pass|skilled), and y= Pr(pass|unskilled) Without the test, Chris’ friend is believed (by both Chris and her supervisor) to be skilled with probability 0.1. If a skilled candidate is hired, the supervisor gets a payoff of 20. If an unskilled candidate is hired, the supervisor gets a payoff of -10, If no one is hired, the supervisor’s payoff is 0. Chris wants to maximize the probability of her friend being hired. (a) Would the supervisor hire Chris’ friend without the test? (b) How would Chris design this test? In other words, what is theoptimal value of x and y?

Chris recommends her friend to her supervisor for a job. To make her recommendation credible, she can design a test for her friend to take. She can choose the difficulty level of the test by choosing the following two parameters: X = Pr(pass|skilled), and y= Pr(pass|unskilled) Without the test, Chris’ friend is believed (by both Chris and her supervisor) to be skilled with probability 0.1. If a skilled candidate is hired, the supervisor gets a payoff of 20. If an unskilled candidate is hired, the supervisor gets a payoff of -10, If no one is hired, the supervisor’s payoff is 0. Chris wants to maximize the probability of her friend being hired. (a) Would the supervisor hire Chris’ friend without the test? (b) How would Chris design this test? In other words, what is theoptimal value of x and y?

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

Ali has taken two books with him for holiday. The probability of liking the first book is 0.5, the probability of liking the second book is 0.4, the probability of liking both books is 0.3. What is the probability that Ali does not like both books?
Dash and Lily Corporation wanted to raise funds for the poor. The first prize for a raffle is S500,000 (with a probability of 0.001) and the second prize is S250,000 (with a probability of0.003). What is a fair price to pay for a single ticket in this raffle?
A recent survey showed that 17% of community college students experienced at least some homelessness during their first year at a community college. Surveys also show that 80% of community college students need to take English their first year at a CC. Based on these surveys what is the probability of first year CC students experiencing at least some homeless during their first year and taking an English class? Show the formula, the math plug-ins, and answer.
Delaney is about to take a final exam that consists of 20 questions. To motivate her to study, her parents promised her $500 if she gets at least 17 questions right. The questions are multiple choice and the probability of her getting a question right is 0.75 on each question of the final exam. What is the probability that she gets exactly 17 questions right? What is the probability that she gets at least 17 questions right?
A surgical technique is performed on seven patients. The technique has a 70% chance of success. Find the probability that the surgery is successful for at least five patients.
Lydia is a project manager and submitted proposals for two different projects, Project X and Project Y to her boss. The probability of getting project X approved is 0.65. The probability of getting project Y approved is 0.77. The probability of getting at least one of the projects approved 0.90. The two projects are independent. True or False
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
In a three subject class setting, there is a 60% chance that the students willpass only two subjects, and 20% of the students will pass only one subject.Determine the probability of the students passing all three subjects.
There are 2 different fire alarm systems in the store. System A detects fire with a probability of 0.67 and costs 2 times cheaper as system B. System B detects fire with a probability of 0.9. Which option is better: to set one system B or two system A?
John can take one of two highways, Interstate A and Interstate B, to get to work each day. The probability that there will be a traffic jam on Interstate A on a given day is 0.65, and the probability that there will be a traffic jam on Interstate B is 0.2. The probability that there will be a traffic jam on at least one of Interstate A or Interstate B is 0.8. Determine the probability that both Interstate A and B will be congested. 0.235 None in the list 0.050 0.062 0.765 Submit Answer Tries 0/3 Determine the probability that Interstate B is congested given that Interstate A is congested. 0.250 0.077 0.812 0.062 None in the list Submit Answer Tries 0/3 Determine the probability that there is a traffic jam on Interstate A given that at least one of the Interstates has a traffic jam. 0.062 None in the list 0.250 0.812 0.077
A bag contains (x + 1) yellow balls, x black balls and (x – 1) white balls. Probability of getting a yellow ball is (2/15) more than that of getting a white ball. Find the value of x.
Please show your solution. A petroleum company exploring for oil has decided to drill 2 wells, one after the other. The probability of not striking oil in the first well is 0.25. Given that they strike oil in the first attempt, the probability of striking oil in the second attempt is 0. 85. What is the probabilty of striking oil in both wells?