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Mastering Probability for Business Decisions, Lecture notes of Probability and Statistics

University of DerbyProbability and Statistics

This lecture note is your ultimate guide to mastering basic probability concepts essential for quantitative decision-making in business. It breaks down key topics with clarity. Core concepts include: Probability Fundamentals: Single, joint, and conditional probabilities explained. Rules of Probability: Subtraction, addition, and multiplication rules for event likelihoods. Contingency Tables: Organizing and analyzing probabilities with tables. Expected Value Model: A weighted average approach to evaluate uncertain outcomes. Independent vs. Dependent Events: Understand how events interact and affect probabilities. Additionally, it includes a list of definitions of these theories and a list of relevant equations. Textbook used to integrate these notes with: Levine, D, Stephan, D, & Szabat, K 2020, Statistics for Managers Using Microsoft Excel, Global Edition, Pearson Education, Limited, Harlow. Available from: ProQuest Ebook Central

Typology: Lecture notes

2023/2024

Available from 12/19/2024

amnah-asghar
amnah-asghar 🇬🇧

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21/10/2024
QUANTITATIVE SKILLS FOR BUSINESS: Lecture 1: BASIC PROBABILITY
DEFINITIONS:
Single event: Event described by single characteristic
Joint event: Described by two or more characteristics
Complement of an event A (A’): Events that are not part of A
Probability: A Numerical value representing the possibility that an event will take place.
Impossible event: No chance of occurring
Certain event: An event that will occur with probability equals to 1
Mutually exclusive: Events that cannot occur simultaneously
Collectively exhaustive events: One of the events must take place
More on subjective probability;
•is based on a person’s point of view of the situation
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QUANTITATIVE SKILLS FOR BUSINESS: Lecture 1: BASIC PROBABILITY DEFINITIONS: Single event: Event described by single characteristic Joint event: Described by two or more characteristics Complement of an event A (A’): Events that are not part of A Probability: A Numerical value representing the possibility that an event will take place. Impossible event: No chance of occurring Certain event: An event that will occur with probability equals to 1 Mutually exclusive: Events that cannot occur simultaneously Collectively exhaustive events: One of the events must take place More on subjective probability; •is based on a person’s point of view of the situation

JOINT PROBABILITY:

  • events can be placed in a contingency table •marginal probability: Referred to total margins, can be found using the following: ~the probability of any event to occur is always between 0 and 1 ~the sum of all mutually exclusive and collectively exhaustive events is always 1

REMINDER OF TYPE OF EVENT

- Subtraction Rule ‘not happen’ statements P[  **E] = 1 - P[E]

  • Addition Rule for ‘or’ statements P[A or B] = P[A] + P[B] if mutually exclusive P[A or B] = P[A] + P[B] – P[A and B] if not mutually exclusive
  • Multiplication Rule for ‘and’ statements P[A and B] = P[A] x P[B] if independent P[A and B] = P[A] x P[B/A] if not independent** When the probability of an event is known, the expected value model can be used. It is used when the probability and the value of a pathway and work out the value of that uncertain outcome, it’s a weighted average that depends on its probability, to calculate of multiply the value of the outcome by the probability. Where:

P(x) is the probability x is the value of each outcome