Bayes theorem explained. Bayes’ Theorem Bayes’ theorem provides a systematic way to compute the probability of a given event A by incorporating available information about another event B. For example: if we have to calculate the probability of taking a blue ball from the second bag out of three different bags of balls, where each bag contains three different colour balls viz. Benefits and challenges in data science, medicine, and more. In this video, I solve a Naive Bayes numerical step-by-step using Bayes Theorem and the Law of Total Probability If you are preparing for: • GATE 2026 • CUET PG • Machine Learning exams The typical behavior of the majority, i. You may already be familiar with probability in general. Speaker: Ian Olasov, City University of New York Bayes' Theorem of Probability With Tree Diagrams & Venn Diagrams Introduction to Bayesian data analysis - part 1: What is Bayes? Conditional probability visualized using trees. red, blue, black. We try to use simple and intuitive examples to illustrate what it does and why it is important. Feb 10, 2026 · Bayes' theorem is a statistical formula used to calculate conditional probability. In this video, you’ll learn: What Bayes’ Theorem really means Why intuition often fails in probability The idea of prior, likelihood, and posterior Simple real-life applications (medical tests Can a "naive" assumption actually be brilliant? In this deep dive, we explore Naive Bayes, one of the most efficient and robust classification algorithms in In this video, we explain the Naive Bayes Theorem, its intuition, and different types of Naive Bayes algorithms, including Bernoulli Naive Bayes and Multinomial Naive Bayes, with clear examples. Bayes' Theorem Explained with Detailed Examples Bayes' Theorem is a fundamental concept in probability theory used to find conditional probabilities. Bayes theorem is also known as the formula for the probability of “causes”. co/patreonmore French mathematician Pierre-Simon Laplace independently published the rule in his 1814 work Essai philosophique sur les probabilités. Frequentist inference is aimed at given procedures with frequency guarantees. These are idfferent things and there is no reason to expect them to be the In this Wireless Philosophy video, Ian Olasov (CUNY) introduces Bayes' Theorem of conditional probability, and the related Base Rate Fallacy. 05M subscribers Subscribe Bayes' Theorem Articles An Intuitive (and Short) Explanation of Bayes’ Theorem Understanding Bayes Theorem With Ratios “If you can't explain it simply, you don't understand it well enough. So how does it work? Bayes theorem, the geometry of changing beliefs 3Blue1Brown 8. See how a cancer test scenario illustrates the equation and the intuition behind it. In this video, we will go over the Bayes' theorem or the Bayes' rule. PROBABILITY RULES, CONDITIONAL PROBABILITY AND BAYES’ THEOREM Step-by-Step Examples and Applications 1. Learn how to use Bayes' theorem to correct for test errors and find the real probability of an event. The ideas involved here are not new, and most of these problems can be solved using a tree diagram. Probability tells us how often some event will happen after many repeated trials. A) Explain the following i) Central limit theorem ii) Bayes' theorem B) In a certain manufacturing facility, three machines, A1, A2, and A3 produce 50%, 30%, and 20%, respectively, of the total products. UNIT-IV 5a) i) Define frequent itemset and explain support and confidence. Our visual guide uses simple shapes to make it intuitive. Bayes' theorem (alternatively Bayes' law or Bayes' rule), named after Thomas Bayes (/ beɪz /), gives a mathematical rule for inverting conditional probabilities, allowing the probability of a cause to be found given its effect. Bayes Theorem Bayes theorem is a theorem in probability and statistics, named after the Reverend Thomas Bayes, that helps in determining the probability of an event that is based on some event that has already occurred. Bob picks at random. The theorem provides a mathematical framework for adjusting initial beliefs If you ever came across Bayes’ theorem, chances are you know it’s a mathematical theorem. Bayes' theorem describes the probability of an event, based on prior knowledge of conditions that might be related to the event. $$ p (A|B) = \frac { p (A) \cdot p (B|A) } { p (B) } $$ p (A|B) and p (B|A) are conditional probabilities (posterior probabilities) p (A) and p (B) are marginal probabilities (prior probabilities) In essence, Bayes’ theorem Data scientists rely heavily on probability theory, specifically that of Reverend Bayes. In this section, we will develop and use Bayes' theorem to solve an important type of probability problem. The numerical results are discussed to highlight practical Bayes' theorem (also known as the Bayes Rule or Bayes Law) is used to determine the conditional probability of event A when event B has already occurred. 🌐 **Understanding Bayes' Theorem in Probability and Statistics** 📊 Bayes' Theorem is a fascinating concept in the realm of probability and statistics that allows us to flip conditional probabilities based on new information. Finally, understand the proof of Bayes' Theorem without dense math. It is simple, elegant, beautiful, very useful and most… Bayes’s Theorem is very important in machine learning due to its process of reasoning with uncertain information – thus letting computers make good decisions based on probabilities. Bayes’ Theorem is widely used in various applications like medical diagnosis, spam filtering, and even in artificial intelligence for decision-making processes. First, I will give a simple description of the theorem, followed by a real-life example That’s where Bayes’ Theorem comes in – it gives us a quantitative framework for updating our beliefs as the facts around us change, which in turn allows us to improve our decision making over time. From historical data, it is known that 1%, 4%, and 3% of the products made by each machine respectively are defective. ii) Discuss rule-based classification and its advantages. e. Bayes theorem was formulated by Reverend Thomas Bayes, an 18th-century British statistician and Presbyterian minister. 1. Mar 11, 2025 · In this article, we will explain Bayes' Theorem. Bayes' Theorem, often lauded as a fundamental pillar of statistical inference, offers a powerful framework for updating our beliefs about. . Learn how to solve any Bayes' Theorem problem. It adjusts probabilities when new information comes in and helps make better decisions in uncertain situations. Introduction Probability measures the likelihood that an event will occur. A visual way to think about Bayes' theorem, and strategies for making probability more intuitive. It explains how to use the formula in solving example problems in addition to usin Bayes' Theorem is one of the most central ideas in all of probability and statistics, and is one of the primary perspectives in modern machine learning too. Learn how Bayes’ Theorem helps in making s Dynamic mechanics of BAYES THEOREM EXPLAINED WITH EXAMPLE Overview and Information Detailed research compilation on Dynamic mechanics of BAYES THEOREM EXPLAINED WITH EXAMPLE synthesized from verified 2026 sources. Learn how to use Bayes' Theorem to calculate probabilities when you know certain other probabilities. Learn how to derive the formula, its use cases and use in machine learning, and its pros and cons. In general, these are differ-ent, A lot of confusion would be avoided if we used F (C) to denote frequency probablity and B(C) to denote degree-of-belief probability. Today, Bayes' Rule has numerous applications, from statistical analysis to machine learning. Bayes' Theorem is the foundation of Bayesian Statistics. Understand Bayes’ Theorem easily: step-by-step formula, clear examples, and practical uses for Class 12, JEE, and everyday probability problems. Dec 6, 2025 · Bayes' Theorem is a mathematical formula used to determine the conditional probability of an event based on prior knowledge and new evidence. ” —Einstein (more) Bayes' theorem helps calculate conditional probability. Bayes Theorem is probably one of the most important things any rational person can learn, because so many of our debates and disagreements that we shout at each other about are because we don’t understand how our beliefs work. [3][4] For example, in Bayesian inference, Bayes' theorem can be used to estimate the parameters of a probability distribution or statistical model. Check out Audible: http://ve42. For a comple Understand Bayes' theorem in machine learning, its formula, significance, and how it helps in probabilistic predictions and classification. Bayes' Theorem can be confusing. ii) Discuss tree pruning methods and their importance. In Harry Potter and Learn how Bayes' theorem transforms decision-making with this essential guide. Bayesian inference is about stating and manipulating subjective beliefs. It’s used in many areas, like medicine and artificial intelligence, and helps us make better decisions. Bayes' theorem is a method of calculating the conditional probability P (F | E) from P (E | F). This article will explain Bayes' Rule in plain language. This video was you through, step-by-step, how it is easily derived and why it is useful. Bayes' Theorem is a fundamental concept in probability theory used to find conditional probabilities. In the first game, Bob first picks one of two coins: an unfair heads-heads coin and a fair heads-tails coin. co/audible Support Veritasium on Patreon: http://ve42. When flipping the coin, Bob flips only the original coin that was picked. See examples of fire, smoke, rain, cloud, pink, man, allergy and test, and how to avoid false positives and negatives. The general statement of Bayes’ theorem is “The conditional probability of an event A, given the occurrence of another event B, is equal to the product of the probability of B, given A Bayes’ Theorem lets us look at the skewed test results and correct for errors, recreating the original population and finding the real chance of a true positive result. You've experienced probability when you've flipped a coin, rolled some dice, or looked at a weather forecast. Bayes’s theorem, in probability theory, a means for revising predictions in light of relevant evidence, also known as conditional probability or inverse probability. Then he flips the coin multiple times (2 times in the video). We’ll look at how it works and explore real-life examples. Sounds intimidating, but we'll walk you through it. , not switching, may be explained by phenomena known in the psychological literature as: The endowment effect, [28] in which people tend to overvalue the winning probability of the door already chosen – already "owned". Use this brief guide to learn about Bayes' Theorem. This page provides a clear explanation of the theorem, visual diagrams, and multiple solved examples with step-by-step solutions. It’s most commonly associated with using evidence for updating rational beliefs in hypotheses. Conditional probability The first concept to understand is conditional probability. Solved Example Naive Bayes Classifier to classify New Instance PlayTennis Example by Mahesh HuddarHere there are 14 training examples of the target concep What is Bayes' Theorem? To best understand Bayes' Theorem, also referred to as Bayes' Rule, I find it helpful to start with a story. This theorem has a central role in probability theory. This tutorial first explains the concept behind Bayes' Theorem, where the equation comes from, and finally how to use the formula in an example. (OR) 4b) i) Explain Naïve Bayes classification using Bayes theorem. In this video, we explore Bayes’ Theorem — one of the most powerful concepts in probability and logical reasoning. In the second game, Bob chooses from three coins: a fair coin, another fair coin The decisions we make in life often come down to Bayes’ Theorem, but most of us don’t even realise what it is. Bayes’ Theorem is an important idea in probability that helps us change our predictions or beliefs when we get new information. This video tutorial provides an intro into Bayes' Theorem of probability. Bayes' theorem explained with examples and implications for life. While this post isn’t about listing its real-world applications, I’m going to give the general gist for why […] Bayes’ theorem is one of the most fundamental theorem in whole probability. Bayes' theorem describes the conditional probability of an event based on data as well as prior information or beliefs about the event or conditions related to the event. UNIT-III 4a) i) Explain Decision Tree Induction algorithm with a sample dataset. Get the definition of Bayes' theorem and learn how to use it to calculate the conditional probability of an event. Go deeper with your understanding of probability as you learn about theoretical, experimental, and compound probability, and investigate permutations, combinations, and more! Q2. Learn how it works, how to calculate it step by step, and see real-world examples. ojryo, jsqkfp, z1vc, jvyvn, cco3, c6wl3, i76j9, ylwhf, tgqzz, jp5a2,