Basic probability theory ppt. steps hazard identification, exposure.

0 ≤ pr (A) ≤ 1 2. Probability and Uncertainty Probability measures the amount of uncertainty of an event: a fact whose occurrence is uncertain. Sample Spaces . Aug 17, 2023 · Introduction to Statistics is a resource for learning and teaching introductory statistics. Conditional probability considers the probability of one event occurring given that another event has Title: Basic principles of probability theory 1 Name Garib Murshudov (when asking questions Garib is sufficient) e-mail garib_at_ysbl. The probability that a large earthquake will occur on the San Andreas Fault in Description: This file contains the information regarding theory of probability, lecture slide 1. ). Dependent and independent events. 267, it can be reported as . For more topics stay tuned with Learnbay. • Probability and Statistics for Engineering and the Sciences by Jay L. Random experiments 2. 1 Elements of probability In order to define a probability on a set we need a few basic elements, Sample space Many basic probability problems are counting problems. Read more. It refers to the frequency at which some events or experiments occur. An estimate of the probability of occurrence and. 2 Probability Probability is a numerical measurement of likelihood of an event. the empty set. Find the probability of each outcome. The probability of a specified event is the chance or likelihood that it will occur. This resource is a companion site to 6. empirical probability • 3. The symbol for denoting union of sets is ‘∪‘. Bayes' theorem is also known as Bayes' rule, Bayes' law, or Bayesian reasoning, which determines the probability of an event with uncertain knowledge. severity of the consequences of exposure to a. Axiom 2: P(Ω) = 1. There are three types of probability: theoretical, experimental, and subjective. Theory of Probability, Lecture Slide 39. If you randomly pick up the ball from any bag (without Oct 5, 2009 · 2. The theory of probability has always been associated with gambling and many most accessible examples still come from that activity. A function from I to M is a rule that associates to each element of I a corresponding element of M. Last Lecture (PDF) This section provides the schedule of lecture topics and the lecture slides used for each session. 426 views • 22 slides Oct 4, 2021 · This presentation guide you through Basic Probability Theory and Statistics, those are Random Experiment, Sample Space, Random Variables, Probability, Conditional Probability, Variance, Probability Distribution, Joint Probability Distribution, Conditional Probability Distribution (CPD) and Factor. potx file. The most popular theory posits that the dinosaurs were killed by the ensuing environmental catastrophe. Sc , M. ppt, Subject Mathematics, from Indian Institute of Technology, Kharagpur, Length: 46 pages, Preview: DR. regardless of the value the other r. For more topics stay adjusted with Learnbay. More Brownian Motion (PDF) 38. P (A and B) = P (A) x P (B) or P (A∩ 𝐵) = 𝑃 (𝐴) ∙ 𝑃 (𝐵) 21. ppt from DEPARTMENT OF MATHEMATICS 271 at University of Dar es salaam. One would be experimental in nature, where we repeatedly conduct an experiment. Basic probability theory • Definition: Real-valued random variableX is a real-valued and measurable function defined on the sample space Ω, X: Ω→ ℜ – Each sample point ω ∈ Ω is associated with a real number X(ω) • Measurabilitymeans that all sets of type belong to the set of events , that is {X ≤ x} ∈ that students are already familiar with basic probability theory. Best applied to processes which can be repeated many times , independently , and under the same conditions . Therefore, in this third part, we assume that the reader is familiar with the View Notes - 1. 36. u k location Bioscience Building (New Biology), Course Description. It discusses: 1. ppt), PDF File (. For example: consider that you have two bags, named A and B, each containing 10 red balls and 10 black balls. xp(X = x;Y) For discrete r. Example: Assume there are 1 man and 2 women in a room. The probability of an event is a number indicating how likely that event will occur. Probability of an Event Not Occurring: If you want to find the probability of an event not happening, you subtract the probability of the event happening from 1. If a probability is determined to be, say, P (A) = . It can be written as a fraction, decimal, percent, or ratio between 0 and 1. It was presented by P. F- Test 8. (IITK) Basics of Probability and Probability Distributions 7. Here there are no possible outcomes in the event. e. Events are collections of outcomes. Find the probability of throwing an 8 on a normal die. Sample space: The collection of all possible events is called sample space. Jeff draws balls from the jar below. characterization. takes For discrete r. Probability tells us how often some event will happen after many repeated trials. It covers counting sample points using tree diagrams, multiplication rules, permutations, and combinations. The higher the probability of an event, the more likely it is that the event will occur. The only other thing that I need to point out is that probability theory allows you to talk about non elementary events as well as elementary ones. Example 1: finding the probability of an event a. The meaning of probability is basically the extent to which something is likely to happen. Hence the probability of throwing an 8 is 0 6 =0. We will give a very quick review; some references for further reading appear at the end of the chapter. it is the sum of the PMF table along the Presentation on theme: "Basic Probability Concepts"— Presentation transcript: 1 Basic Probability Concepts Objective. Probabilities can but need not be rounded. Part of the process of Risk Analysis. 1: The Basics of Probability Theory. 00. Even More Brownian Motion (PDF) 39. yp(X;Y = y); p(Y) = P. Sample space 3. 041SC Probabilistic …. subjective probability. Use probability theory as a formal means of manipulating degrees of belief Given a proposition, A, assign a probability, P(A), such that 0 = P(A) = 1, where if A is true, P(A)=1, and if A is false, P(A)=0. It discusses key probability concepts like: - Probability is defined as the number of desired outcomes divided by the total number of possible outcomes and must be between 0 and 1. Axiom 3: If A1,A2, . 4 red. Traditional queuing theory problems refer to customers visiting a store, analogous to requests arriving at a device. 267 or rounded to . In these notes, we provide a basic treatment of probability that does not address these finer details. Aug 21, 2014 · Some basic Probability Rules Rule 1: The probability of any event E is a number between and including 0 and 1. It helps finding all the possible values a random variable can take between the minimum and maximum statistically possible values. BASIC NOTIONS OF PROBABILITY THEORY. Random experiments, sample spaces, events, and the classification of events as simple, mutually exclusive, independent, and exhaustive. C = "Sum of two dice is divisible by 4". May 22, 2015 · Probability is the mathematics of chance that describes the likelihood of events. Examples are provided for each concept to illustrate The document defines basic probability concepts such as experiments, sample spaces, simple events, events, complements, and subjective and objective views of probability. OCW is open and available to the world and is a permanent MIT activity. Oct 17, 2019 · probability. The tools of probability theory, and of the related field of statistical inference, are the keys for being able to analyze and make sense of data. 2 Sampling with replacement Let Ibe a set with nelements and let Mbe a set with melements. 1 Basic Definitions. Typically these axioms formalise Part I: The Fundamentals. A probability of 1 is equivalent to 100% certainty. 28). 1 A PowerPoint template is a pattern or blueprint for your slides that you save as a . probability theory) and the integral theory as a Daniell functional. 141 likes • 54,512 views. The are various other Nov 20, 2023 · Introduction to Basics of Probability Theory. The three main approaches to defining probability: classical, relative frequency, and subjective. To find the union of two given sets A and B is a set which consists of all the elements of A and all the elements of B such that no element is repeated. 1 Events and Complements (2/6) • A sample space consists of eight outcomes with a probability value. THIAGARAJAN ASSOCIATE PROFESSOR OF MATHEMATICS ST JOSEPH'S COLLEGE TRICHIRAPPALLI Uncertainty in AI Outline: Introduction Basic Probability Theory Probabilistic Reasoning Why should we use probability theory? Jan 1, 2013 · The most significant fundamental concepts of the theory of probability applied in structural reliability include: Experiment; Random event; and. Create a sample space with equally likely outcomes for a spinner with 4 sections numbered 1,2,3,4. ? If the trial consists of ipping a coin twice, the . ? Trials refers to an event whose outcome is un-known. txt) or view presentation slides online. You pick a person randomly. Examples are provided to illustrate different ÐÏ à¡± á> þÿ C E þÿÿÿX Y Z [ D F ý Jul 16, 2017 · In words, we divide probability of both Rain and Sunny by the probability of a Sunny weather. Additionally, it explains concepts May 26, 2022 · 13. All 6 faces of a die: Title: Basic Concepts of Discrete Probability 1 Basic Concepts of Discrete Probability (Theory of Sets Continuation) 2 Functions. May 12, 2017 · The probability of event A =. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set of axioms. 29). 3 experimental roots. Probability is the measure of the likelihood that an event will occur in a Random Experiment. 1. txt) or read online for free. Queuing Theory Queuing theory is the mathematics of waiting lines. - Tree diagrams can show all Classical Probability (Equally Likely Outcomes): To find the probability of an event happening, you divide the number of ways the event can happen by the total number of possible outcomes. Frequency Theory. steps hazard identification, exposure. Mar 9, 2015 · If events A and B are independent, the probability of both events occurring is found by multiplying the probabilities of the events. , coin flips, packet arrivals, noise voltage • Basic elements of probability: Sample space: The set of all possible “elementary” or “finest grain” A Tutorial on Probability Theory 1. B ∪ C = "Sum of two dice is divisible by 3 or 4". Chapter Five Elementary Probability Theory. Yet many students with backgrounds in linguistics, psychology, or other social sciences (and even some computer science students) have very little exposure to probability theory. Find the probability that he gets a red and then a blue ball, in that order. Jun 11, 2012 · The document provides an overview of key probability concepts including: 1. 37; download. It also defines basic terminology like experiments, trials, outcomes, and events. Topics. The actual outcome is considered to be determined by chance. Jun 23, 2012 · Since there is only one outcome, it is a simple event. An extremely large meteor crashed into the earth at the time of the disappearance of the dinosaurs. probability play a starring role. It defines probability as a measure of how often an event will occur if an experiment is repeated. paired t - Test 7. These terms are used in classical probability theory, but are also applicable in contemporary probability theory based on the theory of sets. Sample space (space of events). He draws two balls, this time with replacement. To Nov 1, 2014 · If the outcomes in a sample space are not equally likely, then you must add the probabilities of all the individual outcomes in E. 2. 1 Basic probability theory Professor Jørn Vatn . • Place 100 marbles in a bag; 35 blue, 45 red and 20 yellow. Step 2: To make our analysis easier, let’s replace each ordered pair with the sum (Figure 7. ’s: p(X) = P. There are several ways of viewing probability. Classical probability • 2. morley; Category. This presentation guide her thrown Basic Probability Theory and Statistics, those are Per Experiment, Sample Distance, Irregular Variables, Probability, Conditional Probability, Variance, Probability Distribution, Joint Probability Distribution, Conditional Probability Distribution (CPD) both Factor. The document defines key probability terms like random experiments, sample spaces, sample points, events, and the different types of events. A variable represents an event (a subset of the space of possible outcomes). 101 likes • 21,457 views. Title: Basic principles of probability theory 1 Name Garib Murshudov (when asking questions Garib is sufficient) e-mail garib_at_ysbl. AI-enhanced description. Oct 26, 2014 •. You need at most one of the three textbooks listed below, but you will need the statistical tables. • An event is said to occur if one of the outcomes contained within the event occurs. It provides an example to calculate unconditional, conditional, and joint probabilities using a table of frequency data. The textbook for this subject is Bertsekas, Dimitri, and John Tsitsiklis. g. The laws of chance; 2 overview. 1 Elementary Probability Theory. Theory of Probability, Lecture Slide 38. The probability that a fair coin will land heads is 1=2. motivation game theory gambling ; apparatuses coins dice ; playing therewith The basic formula for computing binomial coe cients is n k = n! k!(n k)!: (1. pathogen on human health. Events with probability close to zero are less likely to occur. Dec 31, 2018 · This document provides an overview of teaching basic probability and probability distributions to tertiary level teachers. It also covers different types of probability like classical, statistical, and subjective probability. Events and their probability 4. The easiest way to illustrate the concept is with an example. Some properties of the operation of union: (i)A∪B = B∪A (Commutative law) (ii)A∪(B∪C) = (A∪B)∪C (Associative law) 1. These tools underlie important advances in many fields, from the basic sciences to engineering and management. a) discuss laws of probability, which are useful ; b) define combinations (and permutations) c) use a) and b) to develop the binomial distribution, which is useful. Match case Limit results 1 per page. It is extremely useful in predicting and evaluating system performance. 1 Basic De nitions Trials? Probability is concerned with the outcome of tri-als. are disjoint then. Comparison of results of above tests and is useful for B. The probability of any event is a number between zero and one. The probability that a selection of 6 numbers wins the National Lottery Lotto jackpot is 1 in 49 6 =13,983,816, or 7:15112 10 8. Two coins are tossed. Southern Range, Berhampur, Odisha. t - Test 6. ppt - Free download as PDF File (. 0 ≤ P (E) ≤ 1 Rule 2: If an event E cannot occur, which means the event E is not in the sample space, then its probability is 0. Types of probability • Three types of probability: • 1. Events with probability close to one are more likely to occur. We will assign a real number P(A) to every event A, called the probability of A. 233 kB. empty set = null set = a set with no elements, denoted by space = the set with all the This presentation guide you through Basic Probability Theory and Statistics, those are Random Experiment, Sample Space, Random Variables, Probability, Conditional Probability, Variance, Probability Distribution, Joint Probability Distribution, Conditional Probability Distribution (CPD) and Factor. 0 < P (E) < 1 2. P ( ) = 0 3. Oct 21, 2020 · This presentation covered the following topics : 1. Probability is a number between 0 and 1. P (S) = 1. B = "Sum of two dice is divisible by 3". It gives detail description about probability, types of probability, difference between mutually exclusive events and independent events, difference between conditional and unconditional probability and Bayes' theorem. Basic Probability Concepts: Sample Spaces and Events, Simple Probability, and Joint Probability, Conditional Probability Bayes ’ Theorem Probability Distribution. Marginal Probability Distribution. Sample Space (S)? Set of all possible elementary outcomes of a trial. v. This document provides an overview of probability concepts including: - Probability is a numerical measure of the likelihood of an event occurring, ranging from 0 (impossible) to 1 (certain). Mar 24, 2018 · 11. The sum of these probabilities is 1. It introduces key concepts such as random experiments, sample spaces, events, assigning probabilities, conditional probability, independent events, and random variables. Apr 6, 2019 · The probability of an event is obtained by summing the probabilities of the outcomes contained within the event A. u k location Bioscience Building (New Biology), Mar 24, 2019 · This document provides an overview of probability theory, including key definitions, concepts, and calculations. Probability theory is important to empirical sci-entists because it gives them a rational frame w ork to mak e inferences and test Sep 4, 2012 · Probability- General Rules 1. Set books The notes cover only material in the Probability I course. Take for example the probability of rolling a dice and getting a 2 for the first time and for the second time. 3) Note the important identity n k = n n k : (1. 3 blue. Queuing theory has been used for operations research, manufacturing and systems analysis. EE 178/278A: Basic Probability Page 1–5 Elements of Probability • Probability theory provides the mathematical rules for assigning probabilities to outcomes of random experiments, e. However, we would appreciate a citation where possible. I have taught students like these in courses on NLP and computational cognitive science, Title: Basic Probability 1 Basic Probability. The spinner at the right is spun twice. B ∩ C = BC = "Sum of two dice is divisible by 3 and 4". • Basic Properties of Probability – Assume that S is a sample space for some experiment and E is an event in S. Jul 30, 2012 • Download as PPT, PDF •. Does the fossil record confirm that the disappearance of the dinosaurs was suitably instantaneous? A. Probability theory or probability calculus is the branch of mathematics concerned with probability. 3. Jun 5, 2017 · Probability 10th class. 2 Complementary events If the event is neither impossible nor certain, then clearly its probability is between 0 and 1. Probability theory pro vides a mathematical foundation to concepts such as Òproba-bilityÓ, ÒinformationÓ, Òbelief Ó, ÒuncertaintyÓ, Òcon Þ denceÓ, ÒrandomnessÓ, Òv ari-abilityÓ, ÒchanceÓ and ÒriskÓ. This document discusses basic concepts of probability taught in a class. MIT OpenCourseWare is a web based publication of virtually all MIT course content. What is the probability P 1 that this is a man? If you pick two persons randomly, what is the probability P 2 that these are a man and woman Answer: You have the possible outcomes: (M), (W1), (W2) so P 1 = p(X = x;Y = y)dxdy = 1. Classical probability • P (E) = # of outcomes in E___________ • Total # of outcomes in sample space • You roll a six-sided die. Sc mathematics and statistics students. Ec = "Sum of two dice different from 7". 27. Let’s shade those in (Figure 7. - An experiment generates outcomes that make up the sample space. Probability theory helps explain genetic theory. Balaji P. It also covers marginal, conditional, and joint probabilities as well as the multiplication rule, addition rule, and how they apply to dependent and independent events. A mathematical approach to making the notion of “chance” rigorous. Collection of all Possible Outcomes e. Proposition A must be either true or false, but P(A) summarizes our degree of belief in A being true/false. Brajesh Kumar Jha Page 36 Theorems on Probability Theorem 1 If A is any event defined on finite sample space U, then ( ) ( )APAP −= 1' Where A’ is the complementary event of A. Then. Jul 31, 2012 · Probability concept and Probability distribution. The probability that a drawing pin will land ‘point up’ is 0:62. To learn probability theory and sample space concepts as they pertain to quantifying uncertaint. It discusses basic probability concepts like Jun 27, 2017 · A Probability Distribution is a way to shape the sample data to make predictions and draw conclusions about an entire population. Abhishekkumarkushwah7. All the Probability PowerPoint templates are natively built in PowerPoint, using placeholders on the slide master, color palettes, and other features in PowerPoint, and can contain layouts, theme colors, theme fonts, theme effects, background styles, and even content (according to Microsoft Jun 23, 2017 · Probability Mmedsc Hahm. Download File. Go deeper with your understanding of probability as you learn about theoretical, experimental, and compound probability, and investigate permutations, combinations, and more! Feb 15, 2024 · Document Probability theory. ppt - Free download as Powerpoint Presentation (. 2 yellow. The videos in Part I introduce the general framework of probability models, multiple discrete or continuous random variables, expectations, conditional distributions, and various powerful tools of general applicability. P (E) = 0 Rule 3: If an event E is certainly occur, then its probability is 1. The Probability of an Event because the number of outcomes in an event must be less than or equal to the number of outcomes in the sample space, the probability of an event will always be a number between 0 and 1, that is, 0≤P (E)≤1. Jan 14, 2011 · probability ppt. Basic Probability. Probability and Statistics for Data Science - Spring 2016 Lecture Slides (1) Probability Theory . List all outcomes: Mar 27, 2018 · Any probability discloses a pattern of behavior that is expected to occur in the long run. Basic Probability Basic Concepts Random Experiment is a process leading to at least Jan 25, 2023 · Theorems on Probability: Learn the basic rules of probability, types and theorems, with solved examples from this page. 4) 1. What probability theory is for • Suppose you’ve already texted the characters “There in a minu” • You’d like your mobile phone to guess the most likely completion of “minu” rather than MINUET or MINUS or MINUSCULE • In other words, you’d like your mobile phone to know that given what you’ve texted so far, MINUTE is more likely than Oct 4, 2021 · 6. Moreover, at a certain point, Schwartz’ theory of distributions and discuss elements of the Fourier analysis become useful, and eventually, the reader is referred to our second part-book [96]. The outcome of a random event cannot be determined before it occurs, but it may be any one of several possible outcomes. Intuitively, the probability distribution of one r. Events are called independent if the probability of one event does not influence the other in any way. P (¬A) = probability of a not happening event. Step 3: Since the event we’re interested in is the one consisting of rolls of 4, 5, or 7. P (A) =1, indicates total certainty in an event A. Probability theory is the mathematical framework that allows us to analyze chance events in a logically sound manner. &ndash; A free PowerPoint PPT presentation A Tutorial on Probability Theory 1. Resource Type: Lecture Notes. Basic Probability Theory. The sum of the probabilities of all possible outcomes is 1 or 100%. 1-26; 1-28 (Balasubramanian) 2-2; 2-4 code; 2-9 code; 2-11 code; 2 Review of basic probability theory. 11. assessment, hazard characterization, and risk. The document discusses random experiments, sample spaces Oct 24, 2014 · Basic Probability. Probability is always between 0 and 1, with 1 being a certain event and 0 being an impossible event. 28. Theorem 2 ( ) 10 ≤≤ AP Theorem 3 (a): Addition theorem of probability or theorem of Total Probability. If X is a set and Y is a set, and there is a sequence of well-specified operations for assigning a well-defined object to every element , and by applying these sequence of operations to every member of a set X Jun 13, 2024 · probability theory, a branch of mathematics concerned with the analysis of random phenomena. Jan 8, 2024 · Each event has some probability of occurring: this probability is a number between 0 to 1. set = a collection of objects, denoted by an upper case Latin letter Example: . random variable probability distribution 5. This number is always between 0 and 1, where 0 indicates impossibility and 1 indicates certainty. 670 views • 47 slides Apr 3, 2019 · Probability Theory. The occurrence of R is difficult to predict — we have all been victims of wrong forecasts Theory of Probability, Lecture Slide 37. A classic example of a probabilistic Jul 30, 2012 · Basic Probability. Upload. Probabilities can be expressed at fractions, decimals, or percents. Go Green With Knowledge! Get 30% off on Annual Courses May 17, 2018 · Dr. The word probability has several meanings in ordinary conversation. The text-books listed below will be useful for other courses on probability and statistics. The probability that an event does not occur is 1 minus the probability that it does occur. Brownian Motion (PDF) 37. (also called the complement of A) 19. Probability has been introduced in Maths to predict how likely events are to happen. The document summarizes key concepts in probability and statistics as they relate to biostatistics and medical research. Probability simply talks about how likely is the event to occur, and its value always lies between 0 and 1 (inclusive of 0 and 1). Jan 13, 2015 · This document provides an introduction to probability and its applications in daily life. In probability theory, it relates the conditional probability and marginal probabilities of two random events. Sample space = {1,2,3,4,5,6} Event = {}, i. probability definition, probability theorem, addition theorem , multiplication theorem solved problems Oct 4, 2016 · It defines probability as the likelihood of an event occurring, expressed as a number between 0 and 1. Manjunath from Indira College of Education in Tumkur. york. 6. The probability of an event is between 0 and 1. A scientifically based process composed of 4. Bayes' theorem was named after the British mathematician Thomas Bayes. Equivalently, we can represent the subset via a Probability. element = an object in a set, denoted by a lower case Latin letter We say “ is an element of ,” “ is in ,” or “ belongs to ,” denoted as . ? Trials are also called experiments or observa-tions (multiple trials). Now, each of the 36 ordered pairs in the table represent an equally likely outcome. The document discusses basic probability concepts including classical, relative frequency, subjective probability, and properties of probability. 12. The document defines probability and provides examples of calculating probabilities using tree diagrams and tables. Basic Probability 1. The occurrence of R is difficult to predict — we have all been victims of wrong forecasts The mathematical theory of probability is very sophisticated, and delves into a branch of analysis known as measure theory. Coin tossing Dice rolling (craps) Card games (blackjack, poker, etc. Consider, as an example, the event R “Tomorrow, January 16th, it will rain in Amherst”. pdf. Figure 7. . 1. 672 kB. To qualify as a probability, P must satisfy three axioms: Axiom 1: P(A) ≥ 0 for every A. ac. We hope that the reader has seen a little basic probability theory previously. A given probability can take on a value ranging from 0 to 1. This document provides an overview of probability theory and concepts. i. Probability is quantified as a number between 0 and 1, where, loosely speaking, 0 indicates impossibility and 1 indicates certainty. This work is in the public domain. You've experienced probability when you've flipped a coin, rolled some dice, or looked at a weather forecast. pptx or . Probability of Independent Events Example 1. N. De- Jul 16, 2014 · BASIC NOTIONS OF PROBABILITY THEORY. Event: Each possible outcome of a variable is called an event. Probability. The sum of the probabilities of all possible outcomes in a sample space is 1. It discusses common probability terms like experiment, outcome, sample space, event, and sample point. Documents; view. 639 views • 47 slides Feb 26, 2014 · BASIC NOTIONS OF PROBABILITY THEORY. pdf), Text File (. Suppose you’ve already texted the characters “There in a minu” You’d like your mobile phone to guess the most likely completion of “minu” rather than MINUET or MINUS or MINUSCULE. 676 kB. 2. A fair coin gives you Heads Oct 26, 2014 · Probability basics and bayes' theorem. Jan 3, 2020 · Basic Laws of Probability • The additive law of probabilities: given a set of mutually exclusive events, the probability of occurrence of one event or another event is equal to the sum of their separate probabilities. Definitions of probability, including the frequency and subjective concepts. M. We can find the probability of an uncertain event by using the below formula. Therefore, it can be copied and reproduced without limitation. What probability theory is for. 4. This is the basic probability theory, which is also used in the probability distribution, where you will learn the possibility of outcomes for a random experiment. Theory of Probability, Lecture Slide 1. You should be familiar with the basic tools of the gambling trade: a coin, a (six-sided) die, and a full deck of 52 cards. Example: Selecting From an Jar of Balls. Union, Intersection: For the two dice example, if. P (¬A) + P (A) = 1. lecture Probability_theory. wi sm tb or me lb ro no jn rh