Permutations and Their Theorems Data Science and A.I. Lecture Series Author: Bindeshwar Singh Kushwaha Institute: PostNetwork Academy Theorem 1: Permutations of Distinct Objects The number of permutations of n different objects taken r at a time is: \[ P(n, r) = \frac{n!}{(n-r)!} \] Explanation: First position: n choices. Second position: n-1 choices. Continue until the […]
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Understanding Permutations Data Science and A.I. Lecture Series Author: Bindeshwar Singh Kushwaha PostNetwork Academy Introduction to Permutations A permutation is an arrangement of objects in a specific order. The order of arrangement is crucial in permutations. Example: Arranging the letters of the word “ABC”. Total permutations = $3! = 6$. Key Formula for Permutations The
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Concept of Odds in Favor and Against Data Science and A.I. Lecture Series Author: Bindeshwar Singh Kushwaha Institute: PostNetwork Academy Concept of Odds Odds in Favor and Against Odds in Favor: Ratio of favorable cases to unfavorable cases:\[ \text{Odds in favor of } A = m : (n – m) \] Odds Against: Ratio of
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Probability Problems Based on Classical Definition of Probability Data Science and A.I. Lecture Series Questions What is the total number of outcomes (sample space)? How do we determine favorable cases? How do probability rules apply to the problem? Example: Throwing Two Dice Find the probability of: A doublet (same number on both dice) Sum
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Probability Problem: Throwing a Fair Die Data Science and A.I. Lecture Series Problem Statement A fair die is thrown. Find the probability of: A prime number An even number A number multiple of 2 or 3 A number multiple of 2 and 3 A number greater than 4 Step 1: Sample Space Sample Space:
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Drawing Balls from a Bag Data Science and AI Lecture Series Problem Statement A bag contains: 4 red balls 5 black balls 2 green balls One ball is drawn at random. Find the probability that: It is a red ball. It is not black. It is green or black. Step 1: Total Balls
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Classical or Mathematical Probability Examples Data Science and A.I. Lecture Series What You Will Learn The definition and basic concepts of probability. Examples of classical probability problems. Application of probability rules such as complements and odds. Step-by-step solutions to real-world probability problems. Introduction Probability is the study of uncertainty. It provides tools to measure
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Classical or Mathematical Probability Introduction to Probability Welcome to PostNetwork Academy! This article explains the fundamentals of Classical or Mathematical Probability, including definitions, examples, key characteristics, and limitations. What You Will Learn The definition of Classical Probability and its core formula. Key properties and assumptions of Classical Probability. Examples: Tossing a coin and
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Master Probability Concepts: Exhaustive, Favourable, Mutually Exclusive, and Equally Likely Cases Welcome to the Data Science and AI Lecture Series brought to you by PostNetwork Academy. What Will We Learn? Exhaustive Cases: Understanding the total number of outcomes in a random experiment. Favourable Cases: Identifying outcomes that lead to the occurrence of an event.
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Deterministic to Random: The Role of Probability in AI and Data Science Introduction An experiment refers to an operation or activity that can produce some well-defined outcome(s). Types of experiments: Deterministic Experiments Random (or Probabilistic) Experiments Deterministic Experiments These experiments have a fixed outcome or result, no matter how many times they are repeated
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