the annual demand rate for a product or goods is constant, the inventory model is called deterministic. However, when the demand rate is not constant and not deterministic, the inventory model is called probabilistic and is best described by a probability distribution. The minimum-cost order quantity and re-order policies are based on the assumptions of the demand rate. PROBABILISTIC INVENTORY MODELS 1. A single-period inventory model with probabilistic demand The single-period inventory model
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Outline 4 Probability – the chance that an uncertain event will occur (always between 0 and 1) Impossible Event – an event that has no chance of occurring (probability = 0) Certain Event – an event that is sure to occur (probability = 1) Assessing Probability probability of occurrence= probability of occurrence based on a combination of an individual’s past experience, personal opinion, and analysis of a particular situation Events Simple event
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Unit 2: The Concept of Probability Tammie Shaw BUSN311-1204B-08: Quantitative Methods and Analysis 10/14/2012 Irene Tsapara Abstract This paper will provide you with information on how my probability of getting an “A” in this class is very scarce. You will find out how my other classmates would succeed in this class, and how I would use subjective probability later on in life. There will also be examples of businesses that will use subjective probability within their company. Unit 2: The
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Probability review (week 2) 1 Bernoulli, Binomial, Poisson and normal distributions. In this excercise we deal with Bernoulli, binomial, Poisson and normal random variables (RVs). A Bernoulli RV X models experiments, such as a coin toss, where success happens with probability p and failure with probability 1 − p. Success is indicated by X = 1 and failure by X = 0. Therefore, the probability mass function (pmf) of X is P {X = 0} = 1 − p, P {X = 1} = p (1) A binomial random variable (RV)
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Statistics 100A Homework 5 Solutions Ryan Rosario Chapter 5 1. Let X be a random variable with probability density function c(1 − x2 ) −1 < x < 1 0 otherwise ∞ f (x) = (a) What is the value of c? We know that for f (x) to be a probability distribution −∞ f (x)dx = 1. We integrate f (x) with respect to x, set the result equal to 1 and solve for c. 1 1 = −1 c(1 − x2 )dx cx − c x3 3 1 −1 = = = = c = Thus, c = 3 4 c c − −c + c− 3 3 2c −2c − 3 3 4c 3 3 4 . (b) What is the cumulative
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2. Single Variable Optimisation: Applications 3. Partial Differentiation: Theory and Applications 4. Multivariate Optimisation: Theory and Applications Part B: Probability and Statistics 1. Probability: probability rules, conditional probability, independence. 2. Random Variables: discrete and continuous probability distributions, expectations. 3. Sampling: sampling distributions 4. Confidence Intervals: differences in means 5. Hypothesis Testing: mean, proportions Main
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Value by Gender Gender Mean Extrinsic Value Male 5.33 Female 5.41 The probabilities we looked at were: The probability that the individual would be between 16 and 21 years of age and what the find showed that it would be 12 out of the 44 or 27 percent of the sample. The probability that an individual’s overall job satisfaction is 5.2 or lower was found to be 24 out of 44 or 55 percent of the sample. The probability that an individual will be a female in the human resources department was shown
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Probability & Statistics for Engineers & Scientists This page intentionally left blank Probability & Statistics for Engineers & Scientists NINTH EDITION Ronald E. Walpole Roanoke College Raymond H. Myers Virginia Tech Sharon L. Myers Radford University Keying Ye University of Texas at San Antonio Prentice Hall Editor in Chief: Deirdre Lynch Acquisitions Editor: Christopher Cummings Executive Content Editor: Christine O’Brien Associate Editor: Christina Lepre Senior
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A Solution Manual for: A First Course In Probability: Seventh Edition by Sheldon M. Ross. John L. Weatherwax∗ September 4, 2007 Introduction Acknowledgements Special thanks to Vincent Frost and Andrew Jones for helping ﬁnd and correct various typos in these solutions. Miscellaneous Problems The Crazy Passenger Problem The following is known as the “crazy passenger problem” and is stated as follows. A line of 100 airline passengers is waiting to board the plane. They each hold a ticket to one of
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Probability: Introduction to Basic Concept Uncertainty pervades all aspects of human endeavor. Probability is one of our most important conceptual tools because we use it to assess degrees of uncertainty and thereby to reduce risk. Whether or not one has had formal instruction in this topic, s/he is already familiar with the concept of probability since it pervades almost all aspects of our lives. With out consciously realizing it many of our decisions are based on probability. For example, when
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Probability rules Part I Define the 4 rules of probability. 1. Any probability is a number between 0 and 1 a. P(A) satisfies 0 ≤ P(A) ≤ 1 2. All positive outcomes together must have probability 1 a. P(S) = 1 3. If 2 events have no outcomes in common, the probability that one or the other occurs is the sum of their individual probabilities a. P(A or B) = P(A) + P(B) 4. The probability that an event does not occur is 1 minus the probability that the event does not occur a. P(A does not
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Probability and Statistics for Finance The Frank J. Fabozzi Series Fixed Income Securities, Second Edition by Frank J. Fabozzi Focus on Value: A Corporate and Investor Guide to Wealth Creation by James L. Grant and James A. Abate Handbook of Global Fixed Income Calculations by Dragomir Krgin Managing a Corporate Bond Portfolio by Leland E. Crabbe and Frank J. Fabozzi Real Options and Option-Embedded Securities by William T. Moore Capital Budgeting: Theory and Practice by Pamela P. Peterson
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What are the two basic laws of probability? What are the differences between a discrete probability distribution and a continuous probability distribution? Provide at least one example of each type of probability distribution. The two basic laws of probability are adding mutually exclusive events and addition for events that are not mutually exclusive (Render, Stair & Hanna, 2008). The probability must be between zero and one for any event just as the sum must equal one of all the events. Therefore
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Probability, Mean and Median In the last section, we considered (probability) density functions. We went on to discuss their relationship with cumulative distribution functions. The goal of this section is to take a closer look at densities, introduce some common distributions and discuss the mean and median. Recall, we define probabilities as follows: Proportion of population for Area under the graph of p ( x ) between a and b which x is between a and b p( x)dx a b The cumulative
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Probability & Mathematical Statistics | “The frequency concept of Probability” | [Type the author name] | What is probability & Mathematical Statistics? It is the mathematical machinery necessary to answer questions about uncertain events. Where scientists, engineers and so forth need to make results and findings to these uncertain events precise... Random experiment “A random experiment is an experiment, trial, or observation that can be repeated numerous times under the
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Probability- long run relative frequency. The proportion of times the outcome would occur in a very long series of repetitions Law of large numbers- the long run frequency of repeated events eventually produces the true relative frequency. This is called the empirical probability or objective probability. When we can’t repeat events the probability of an event is called subjective or personal probability. If A and B are disjoint, P(A or B)= P(A) + P(B) General addition rule- P(A or B) = P(A) +
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Mary Reich Math 464-931 Assignment #5 Chapter 18 Review Chapter 18 discussed Theoretical Probability and Statistical Inference. Jakob Bernoulli, wanted to be able to quantify probabilities by looking at the results observed in many similar instances. It seemed reasonably obvious to Bernoulli that the more observations one made of a given situation, the better one would be able to predict future occurrences. Bernoulli presented this scientific proof in his theorem, the “Law of Large Numbers”
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sampling in management research ESS has made a survey created to measure attitudes cross-nationally in Europe, using probability sampling. Measuring an attitude across countries is a tough job, but to successfully apply the methods of probability sampling too, seems close to impossible. This essay will look at the sample-problems that this survey faces, and how a non-probability sample can be successfully integrated. Before starting to analyse the survey, I would like to briefly explain what
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Probability and Distributions Abstract This paper will discuss the trends and data values and how they relate to statistical terms. Also will describe the probability of different actions to the same group of data. The data will be broke down accordingly to qualitative and quantitative data, and will be grouped and manipulated to show how the data in each group can prove to be useful in the workplace. Memo To: Head of American Intellectual Union From: Abby Price Date: 3/05/2014
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American Intellectual Union (AIU) is looking for research data about Gender, Probability factors and several other data sets that they need to use for reporting purposes. This data will help the AIU make sound and responsible decisions in regards to the data that they are looking to collect. Memo To: Director, American Intellectual Union From: John C. Carter Date: 8/2/2014 Subject: Distribution and Probability of data collected Dear Sir: As we discussed in earlier meetings, the
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Probability And Non Probability Sampling Cultural Studies Essay A probability sampling method is any method of sampling that utilizes some form of random selection. In order to have a random selection method, you must set up some process or procedure that assures that the different units in your population have equal probabilities of being chosen. Humans have long practiced various forms of random selection, such as picking a name out of a hat, or choosing the short straw. These days, we tend to
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Assignment 2 Problem 1: Question 1. The probability of a case being appealed for each judge in Common Pleas Court. p(a) | 0.04511031 | 0.03529063 | 0.03497615 | 0.03070624 | 0.04047164 | 0.04019435 | 0.03990765 | 0.04427171 | 0.03883194 | 0.04085893 | 0.04033333 | 0.04344897 | 0.04524181 | 0.06282723 | 0.04043298 | 0.02848818 | Question 2. The probability of a case being reversed for each judge in Common Pleas Court. P® | 0.00395127 | 0.0029656 | 0.0063593
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PROBABILITY 1. ACCORDING TO STATISTICAL DEFINITION OF PROBABILITY P(A) = lim FA/n WHERE FA IS THE NUMBER OF TIMES EVENT A OCCUR AND n IS THE NUMBER OF TIMES THE EXPERIMANT IS REPEATED. 2. IF P(A) = 0, A IS KNOWN TO BE AN IMPOSSIBLE EVENT AND IS P(A) = 1, A IS KNOWN TO BE A SURE EVENT. 3. BINOMIAL DISTRIBUTIONS IS BIPARAMETRIC DISTRIBUTION, WHERE AS POISSION DISTRIBUTION IS UNIPARAMETRIC ONE. 4. THE CONDITIONS FOR THE POISSION MODEL ARE : • THE PROBABILIY
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For Students Solutions to Odd-Numbered End-of-Chapter Exercises * Chapter 2 Review of Probability 2.1. (a) Probability distribution function for Y Outcome (number of heads) | Y 0 | Y 1 | Y 2 | Probability | 0.25 | 0.50 | 0.25 | (b) Cumulative probability distribution function for Y Outcome (number of heads) | Y 0 | 0 Y 1 | 1 Y 2 | Y 2 | Probability | 0 | 0.25 | 0.75 | 1.0 | (c) . Using Key Concept 2.3: and so that 2.3. For the two new random
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Probability Discrete Event Simulation: Tutorial on Probability and Random Variables 1. A card is drawn from an ordinary deck of 52 playing cards. Find the probability that it is (a) an Ace, (b) a jack of hearts, (c) a three of clubs or a six of diamonds, (d) a heart, (e) any suit except hearts, (f) a ten of spade, (g) neither a four nor a club (1/3, 1/52, 1/26, 1/4, 3/4, 4/13, 9/13) 2. A ball is drawn at random from a box containing six red balls, 4 white balls and 5 blue balls. Determine
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the following becomes true fTt=12ttxdx Integrating the above equation, we have; fTt=964t2 Varying the same in the interval2<x<4), we have fTt=12tt38xdx Integrating the equation and solving accordingly we get fTt=-3t264+34 Therefore, probability that a randomly chosen claim on this policy is processed in three hours or more; PrT>3=34(-3t264+34)dt Integrating the equation and solving accordingly we get; PrT>3=34-1-2764 =0.17
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PROBABILITY ASSIGNMENT 1. The National Highway Traffic Safety Administration (NHTSA) conducted a survey to learn about how drivers throughout the US are using their seat belts. Sample data consistent with the NHTSA survey are as follows. (Data as on May, 2015) Driver using Seat Belt? | Region | Yes | No | Northeast | 148 | 52 | Midwest | 162 | 54 | South | 296 | 74 | West | 252 | 48 | Total | 858 | 228 | a. For the U.S., what is the probability that the driver is using
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Probability Distribution in Research Simulation Sheil Merrill RES/341 August 16, 2011 Richard Harrell Aquine is ready to take a greater share of the chronometer market. As you know the chronometer market is the highest priced watch market with chronometers being sold for more than five thousand dollars. It is Aquine’s goal to compete with the established chronometer manufacturers Zweiger, Scheobel, and Waechter. This was the primary reason why Chief Executive Officer Howard Gray hired
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discussing the laws of probability so, in the laws of the probability we have a random experiment, as a consequence of that we have a sample space, we consider a subset of the, we consider a class of subsets of the sample space which we call our event space or the events and then we define a probability function on that. Now, we consider various types of problems for example, calculating the probability of occurrence of a certain number in throwing of a die, probability of occurrence of certain
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7.10.2015 г. 1 1. Experiment, Outcomes, and Sample space 2. Random Variables 3. Probability Distribution of a Discrete Random Variable 4. The Binomial Probability Distribution 5. The Hypergeometric Probability Distribution 6. The Poisson Probability Distribution 7. Continuous Random Variables 8. The Normal Distribution 9. The Normal Approximation to the Binomial Distribution 2 1 7.10.2015 г. An experiment is a process that, when performed, results in one and only one
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be due to the action of a postulated God, making nature, as it were, performing a great symphony” (Swinburne, The Existence of God, 2005). Richard Swinburne approached the argument from the angle of probability suggesting that the evidence of design and order in the universe increases the probability of the existence of God. Swinburne’s argument is based on the remarkable degree and extent of order and regularity in the universe. It is an appealing argument because one cannot deny the apparent evidence
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www.slideshare.net/guest3c11a5/probability-case-study-rheam-smith-gandhotra Case Study 1. Introduction: Great Air Commuter Service is a small regional airline. Provides commuter service between Boston and New York –three round trips daily (total of six flights per day). Promotional contest awarding a large prize to be run one day per month on each flight. The day each month for contest to be run will be selected randomly on the first of each month. On each flight that day, all passengers
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Unit 2 – Probability and Distributions Kimberly Reed American InterContinental University Abstract This week’s paper focuses on an email that will be written to AUI the email will contain information from the data set key and explain why this information is important to the company. Memo To: HR Department From: Senior Manager Date: 20 Sept, 2011 Subject: Data Set Dear Department Heads: The following memo will contain information that contains vital and confidential information
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Title: The Probability that the Sum of two dice when thrown is equal to seven Purpose of Project * To carry out simple experiments to determine the probability that the sum of two dice when thrown is equal to seven. Variables * Independent- sum * Dependent- number of throws * Controlled- Cloth covered table top. Method of data collection 1. Two ordinary six-faced gaming dice was thrown 100 times using three different method which can be shown below. i. The dice was held in
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Probability for Engineers (IHE 6120) Report On Probabilistic Analysis on Revenue generation by Electronic Retailers for five consecutive years Submitted
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CS 70 Discrete Mathematics and Probability Theory Fall 2009 Satish Rao,David Tse Note 11 Conditional Probability A pharmaceutical company is marketing a new test for a certain medical condition. According to clinical trials, the test has the following properties: 1. When applied to an affected person, the test comes up positive in 90% of cases, and negative in 10% (these are called “false negatives”). 2. When applied to a healthy person, the test comes up negative in 80% of cases
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DICE AND PROBABILITY LAB Learning outcome: Upon completion, students will be able to… * Compute experimental and theoretical probabilities using basic laws of probability. Scoring/Grading Rubric: * Part 1: 5 points * Part 2: 5 points * Part 3: 22 points (2 per sum of 2-12) * Part 4: 5 points * Part 5: 5 points * Part 6: 38 points (4 per sum of 4-12, 2 per sum of 3) * Part 7: 10 points * Part 8: 10 points Introduction: While it is fairly simple to understand
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4 6 8 3 12 7 7 8 3 10 3 5 8 7 9 6 6 12 4 7 9 9 11 4 5 2 5 2 3 5 3 10 2 2 4 3 6 3 10 7 7 9 8 5 12 3. (22 pts) Find the experimental probability of rolling each sum. Fill out the following table: Sum of the dice Number of times each sum occurred Probability of occurrence for each sum out of your 108 total rolls (record your probabilities to three decimal places) 2 10 .092 3 13 .120 4 10 .092 5 11 .101 6 9 .083 7 19 .175 8 9 .083 9 9 .083 10 7 .064 11 2
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Their statistics show that an accident prone person will have accident within a year with probability 0.4, whereas probability decreases to 0.2 for a non-accident prone person. If 30% of population is accident prone, what is the probability that a new policy holder will have an accident within one year of purchasing the policy? Suppose a new policy holder has an accident within one year, what is the probability that he or she is accident prone? Q2. Surveys by the Federal Deposit Insurance Corporation
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Probability Distributions Individual Project Tammy Lynn Ayers AIU Online American Inmates Union Data Collection Results Submitted by Tammy Lynn Ayers On November 27, 2011 Dear Mr. Smith, We administered a survey to our inmates in order to measure their satisfaction with their incarceration. From this survey, we collected nine different sections of data. They include: gender, age, types of offense, type of facility, length of sentence, satisfaction with criminal justice system
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Probability and odds are two basic statistic terms to describe the likeliness that an event will occur. In everyday conversation “probability” and “odds” are used interchangeably. If something has a high probability it always also has a high odds of happening. In reality, the Probability of something happening and the odds of something happening are two completely different ways of describing the chances. Simple probability of event A occurring is mathematically defined as: Odds are the ratio
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Using Probability Distribution in Research Jorge Uria RES 341 November 28, 2011 Walter Deckert Background Aquine has been losing market share in the mechanical watch division for the past three years and now stands at five percent. There are different views as to what the reasons for the decline are with some members of management indicating that the quality of manufacture is the problem and others that the advertising strategy is to blame. Research and analysis was conducted on processes
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Chapter 5 Discrete Probability Distributions Learning Objectives 1. Understand the concepts of a random variable and a probability distribution. 2. Be able to distinguish between discrete and continuous random variables. 3. Be able to compute and interpret the expected value, variance, and standard deviation for a discrete random variable. 4. Be able to compute and work with probabilities involving a binomial probability distribution. 5. Be able to compute
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In this discussion I will give a brief summary on the probability of myself receiving an "A" in this class, if I believe that other students can arrive at the same probability, explain what subjective probability means with a business related example and an example of myself using subjective probability in my personal life and how I might use it in the future. MY PROBABILITY OF SUCCESS I really cannot say what my gut feeling tells me on how well I will do. Just by the name of this class made
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Probability XXXXXXXX MAT300 Professor XXXXXX Date Probability Probability is commonly applied to indicate an outlook of the mind with respect to some hypothesis whose facts are not yet sure. The scheme of concern is mainly of the frame “would a given incident happen?” the outlook of the mind is of the type “how sure is it that the incident would happen?” The surety we applied may be illustrated in form of numerical standards and this value ranges between 0 and 1; this is referred to
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PROBABILITY SEDA YILDIRIM 2009421051 DOKUZ EYLUL UNIVERSITY MARITIME BUSINESS ADMINISTRATION CONTENTS Rules of Probability 1 Rule of Multiplication 3 Rule of Addition 3 Classical theory of probability 5 Continuous Probability Distributions 9 Discrete vs. Continuous Variables 11 Binomial Distribution 11 Binomial Probability 12 Poisson Distribution 13 PROBABILITY Probability is the branch of mathematics that studies the possible outcomes of given events together
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Lab I – Probability Models When finished fill in the table at the end of this document and email it to your teacher Cards: Use the tab for Cards in the excel file and get the total probability for the various hands All of your inputs are on the yellow cells (a) The first task is to figure how many chances you have for each pick that will result in a successful hand INPUT: columns B/C/D/E/F (b) Then if any of the events (one of the five cards) has 100% chance then you need multiply
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Probability Question 1 The comparison between the bar chart and histogram are bar graphs are normally used to represent the frequency of discrete items. They can be things, like colours, or things with no particular order. But the main thing about it is the items are not grouped, and they are not continuous. Where else for the histogram is mainly used to represent the frequency of a continuous variable like height or weight and anything that has a decimal placing and would not be exact in other
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minutes Introduction to Probability 1 Probability Probability will be the topic for the rest of the term. Probability is one of the most important subjects in Mathematics and Computer Science. Most upper level Computer Science courses require probability in some form, especially in analysis of algorithms and data structures, but also in information theory, cryptography, control and systems theory, network design, artiﬁcial intelligence, and game theory. Probability also plays a key role in ﬁelds
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Perhaps I shouldn’t have squeezed that extra information out of Xavier after all!” Discuss whether or not Alain is right in thinking that the probability changed from ¼ to ½? ---------------------------------------------- Answer ------------------------------------------------------------ The essence of the problem in Part B is the probability of the selection of one of four individuals for termination. Essentially, one of four members of an analyst team at Quant Investments was going
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