Let us solve some questions based on conditional probability with detailed solutions. 5 Solved Problems. 1). Doob's Inequality, L p Convergence 5. Example 6: What is the number of times a coin needs to be tossed in order to get at least once a head with probability ≥0. A bag contains 5 red sweets and 3 blue sweets. 4 %âãÏÓ 1715 0 obj > endobj xref 1715 21 0000000016 00000 n 0000014010 00000 n 0000014079 00000 n 0000014217 00000 n 0000014306 00000 n 0000014459 00000 n 0000014612 00000 n 0000015048 00000 n 0000028413 00000 n 0000028817 00000 n 0000029193 00000 n 0000029556 00000 n 0000029708 00000 n 0000030380 00000 n 0000048618 00000 n 0000049244 00000 n 0000049723 00000 n 0000050089 00000 n Probabilities: Problems with Solutions. 1. 0 license and was authored, remixed, and/or curated by OpenStax via source content that was edited to the style and standards of the LibreTexts platform. A random variable is some outcome from a chance process, like how many heads will occur in a series of 20 flips, or how many seconds it took someone to read this sentence. Since there are 5 school days in a week, the probability that it is Friday is 0. Find the probabilities a) P (X < 40) b) P (X > 21) c) P (30 < X < 35) A radar unit is used to measure the speeds of cars on a motorway. We observe that p is small and n is large here. About this unit. Each card in a standard deck of 52 playing cards is unique and belongs to 1 of 4 suits: Suppose that Luisa randomly draws 4 cards without replacement. Scroll down the page for more examples and solutions for simple probability. If a customer bought a notebook what is the probability that she also bought a pencil. If the probability of an event is 0, then the event is impossible. Learn and practice basic word and conditional probability aptitude questions with shortcuts, useful tips to solve easily in exams. Example 3: two independent events. 9? Solution: Probability of getting at least one head in n tosses. Complete the tree diagram. 6) 5 (1-0. What is the probability that Luisa gets 2 diamonds and 2 hearts (in any order)? Another example of a continuous random variable is the height of a randomly selected high school student. On the other hand, an event with probability 1 is certain to occur. P (A or B) = P (A) + P (B) Addition Rule 2: When two events, A and B, are non-mutually exclusive, there is some overlap between these events. Conditional Probability Tree Diagram. The mean of our distribution is 1150, and the standard deviation is 150. Bernoulli trials deal with events having clear-cut What is the probability that a randomly selected story will be about Elvis? EXAMPLE 3. Example: your boss (to be fair) randomly assigns everyone an extra 2 hours work on weekend evenings between 4 and midnight. That is: $0 ≤ P(E) ≤ 1$ Common Core: HSS-CP. We can see the applications of probability in many real-life activities. Step 2: Count the number of people who prefer each pet type and then turn the ratio into a probability: People who prefer cats: 7/ May 16, 2024 · Probability Examples and Solutions We have provided you with some probability problems with their solutions. The y -axis contains the probability of x, where X = the number of workers who have only a high school diploma. Jul 7, 2024 · 8th grade probability questions. Give n = 200. The number of adult workers that you expect to have a high school diploma but not pursue any further education is the mean, μ = np = (20) (0. We can compute that by adding ‘offer’ in spam and desired e-mails. 7082 or less is 0. And the probability of getting a head is equal to the probability of getting a tail. Solutions of Chapter 14 Class 11 Probability available free at teachoo. Work out how many black balls are in the bag. For example, let’s say you had the choice of playing two games of chance at a fair. Example 7: The three ships namely A, B, and C May 21, 2022 · Find the probability that the coin lands with a “head”. The probability the first bus will be late is 0. See examples of how to calculate probability for different types of experiments and events. Number of Ace cards in a deck of cards = 4. 100 100. The Bernoulli distribution is a discrete probability distribution that models a binary outcome for one trial. Basic theoretical probability Probability using sample spaces Basic set operations Experimental probability. image by author. Get NCERT solutions of all examples, exercises and Miscellaneous questions of Chapter 13 Class 12 Probability with detailed explanation. Alice has some red balls and some black balls in a bag. There are only two possible outcomes – success and failure, win and lose. The conditional probability, as its name suggests, is the probability of happening an event that is based upon a condition. You have no data to look at, because your business hasn’t been through a recession. (c) The table represents the probability distribution of the random For example, all of the following are subjective probability examples in real life situations: I think that the president has a 25% chance of being elected again. Then the following will be true for the probability of the third event: A) The probability of the third event is greater than the second event. NCERT Solutions Example question: Calculate the marginal distribution of pet preference among men and women: Solution: Step 1: Count the total number of people. In fact, all one-unit ranges in this distribution have the same likelihood of 0. Mary has to catch 2 2 buses to work. We have studied Probability before,Probability is defined asProbability = Example 1: The probability of throwing a 6 sided die and getting a 7. A node is used to represent an event. Solution: Example 3: Find the compound probability of selecting 5 or a black card from a deck. What is the probability that the dart lands inside the circle? Give the exact probability and the probability as a percent rounded to the nearest tenth. Find the probability that a vehicle was used GIVEN THAT it was a van. 9. 0. The random variable R is the score on the red die and the random variable B is the score on the blue die. Consider a WSS random process X(t) with Find the PSD of X(t), and E[X(t)2] . Example 1: There are 8 balls in a container, 4 are red, 1 is yellow and 3 are blue. Oct 2, 2020 · 00:45:53 – Use integration of the exponential distribution density function to find probability (Example #3) 00:49:20 – Generate the exponential cumulative distribution function formulas. Worked-out examples include flipping a coin and rolling a 6-sided die. In this case, there are 3 yellow marbles and a total of 8 marbles. 4. 8. What is the probability of getting an ace of spade, and a card of heart, as first and second card, respectively? Solution 2: Since the cards are drawn without replacement, therefore, both the events are dependent upon each other. There are 3 rooms, 2 suspects, and 1 weapon. Every textbook comes with a 21-day "Any Reason" guarantee. NCERT Solutions For Class 12 Maths Chapter 13 Probability solved by expert Teachers at LearnCBSE. 916. You think that a recession is about to hit, and you want to calculate the impact to your business. This is a conditional probability question. Scroll down the page for more examples and solutions. 5 months ago. Hence, the probability for a value falling between 6 and 7 is 0. Frequently asked simple and hard probability problems or questions with solutions on cards, dice, bags and balls with replacement covered for all competitive exams,bank,interviews and entrance tests. Jake is going to call one person from his contacts at random. For example, we may say that it will probably rain today because most of the days we have observed were rainy days. 0/1600 Mastery points. h. 1 0. %PDF-1. 5. P ( contains offer|spam) = 0. Use it for a random variable that can take one of two outcomes: success (k = 1) or failure (k = 0), much like a coin toss. Example: A single six sided dice is rolled one time. Class 12 Maths Probability NCERT Soutions for CBSE Board, UP Board, MP Board, Bihar, Uttarakhand board and all other boards following new CBSE Syllabus free to download in PDF form. Example 1: What is the probability that a card taken from a standard deck, is an Ace? Solution: Total number of cards a standard pack contains = 52. That transformation appears below. Now, by looking at the formula, Probability of selecting an ace Nov 21, 2023 · Learn formulas and see examples with detailed solutions. B. Solution: Numbers of pens = Numbers of defective pens + Numbers of good pens. Examples, solutions, videos, and lessons to help High School students learn how to apply the general Multiplication Rule in a uniform probability model, P (A and B) = P (A)P (B|A) = P (B)P (A|B), and interpret the answer in terms of the model. This page titled 5. Many real life and business situations are a pass-fail type. Example 1: A bag I contains 4 white and 6 black balls while another Bag II contains 4 white and 3 black balls. A branch is used to denote the connection between an event and its outcome. Also we do not need to divide by \(n - 1\). Jul 13, 2024 · The probability of event or outcome ‘A’ and event ‘B’ happening. Two sweets are drawn at random with replacement. Because each flip is independent, the probability of the first heads is 1/2, and the likelihood of heads on The formulas for the probability distribution function and the probability mass function for a discrete random variable are given below: Probability Distribution Function: F (x) = P (X ≤ x) Probability Mass Function: p (x) = P (X = x) Probability Distribution of a Continuous Random Variable. b) Score: 73%. Work out the probability that at least one bus will be late. Find the probability that it was drawn from Bag I. He has ‍ total contacts. 14) we saw that there were 21 possible storylines. One of these games is a discrete probability distribution and one is a continuous probability distribution. Given a standard die, determine the probability for the following events when rolling the die one time: P (5) P (even number) P (7) Before we start the solution, please take note that: P (5) means the probability of rolling a 5. In general, the higher the probability of an event, the more likely it is that the event will occur. ⇒ n ≥ 3. Addition Rule for OR Events: P(A or B) = P(A) + P(B) – P(A and B) g. Find out the Joint Probability where. Definition A random variable is discrete if. 3. There’s uncertainty in so many fields. 14. Find the probability that the vehicle was used OR a van. Solution: Total number of marble = 10. Determine the probability that a 2 was rolled, GIVEN an even number has been rolled. Let X(t) be a random process with mean function μX(t) and autocorrelation function RX(s, t) ( X(t) is not necessarily a WSS process). Example 3: The probability of living forever. The probability that Alice picks a red ball is x and the probability that Alice picks a black ball is 4x. 2. The probability that X = 5 is given by the binomial probability formula as follows: P (X = 5) = 8 C 5 (0. Probability of solving a specific problem independently by A and B are 1/2 and 1/3, respectively. Let X be the random variable representing the sum of the dice. Probability 5th edition solutions are available for this textbook. All NCERT Questions, Examples and Exercises are solved with step-by-step answers to all questions explained in detail. Problem 1. Geometric Probability Using Area Examples: (1) A circle with radius 2 lies inside a square with side length 6. 2 solution In solving that problem (EXAMBLE 3. It’s the number of times each possible value of a variable occurs in the dataset. 8 (given in the question) P (spam) = 0. For the denominator, you need to calculate 69 C 5, which equals the number of combinations when you draw five numbers from a total of 69 numbers. We want to find the chances of getting heads on both the first and second flips. Solutions to all exercise questions, examples and optional is available with detailed explanations. Calculate probabilities and expected value of random variables, and look at ways to transform and combine random variables. Examples 4. In this chapter, we will study. 6 6. 278691. Example 2: The probability of buying a shirt from a store that only sells shoes. Hugo plans to buy packs of baseball cards until he gets the card of his favorite player, but he only has enough money to buy at most 4 packs. For example, if you flip a coin, you either get heads or tails. So the probability of pulling a yellow marble is 3/8. P (E) = (Number of favourable outcomes/Total number of outcomes) P (picking a good pen) = 132/144 = 11/12 = 0. For example, assume that the probability of a boy playing tennis in the evening is 95% (0. on a given day in a certain area. Mean λ= np = 200 × 0. 12 are green and 9 are blue. Throw a dice 3 times. n ( S) = 100. The value of this random variable can be 5'2", 6'1", or 5'8". Published by Cambridge University Press. This LibreTexts book chapter covers the basic concepts, formulas, examples, and exercises of discrete probability distributions. It is actually the probability or likeliness of the bisection of two or more events. com Step 2: Look for all the available paths (or branches) of a particular outcome. Solution: Total number of cards in a deck = 52 Number of cards in each suit = 13 Determine the probability that the pen taken out is a good one. daniella. . Aug 2, 2020 · In short, it helps us build good expectations about real-world events and phenomena. We started learning about Probability from Class 6,we learned that Probability is Nu Example 3: If 3% of electronic units manufactured by a company are defective. Construct a discrete probability distribution for the same. Formula sheet also available. Find the probability of getting (i) 2 red sweets (ii) 2 the same color (iii) at least one red sweet. However, in mathematics, we would require a more accurate way of measuring probability Updatedaccording tonew NCERT- 2023-24 NCERT Books. Red and Green marbles = 8 We use "P" to mean "Probability Of", So, for Independent Events: P (A and B) = P (A) × P (B) Probability of A and B equals the probability of A times the probability of B. Question 1: Ten numbered cards are there from 1 to 15, and two cards a chosen at random such that the sum of the numbers on both the cards is even. n ( B) = 100 – 60 – 30 = 10. When you see P ( ) this means to find the probability of whatever is indicated Solved Examples Using Conditional Probability Formula. , n (A) = 18 n (B) = 9. f. Uniform Integrability, Convergence in L 1 7. 24. Nov 4, 2021 · Example 1: Weather Forecasting. There are 4 rooms and 5 suspects. 6. 05)/0. its support is a countable set ; there is a function , called the probability mass function (or pmf or probability function) of , such that, for any : The following is an example of a discrete random variable. ⇒ 1 − (1/2) n ≥ 0. This page titled 7. Example 1: A compound event can occur in 3 ways, each of which is equally likely. 30. When the coin is tossed, it lands “tail”. You can apply probability theory in science, games, economics, education, politics, and many more. Those values are obtained by measuring by a ruler. Backwards Martingales 8. Answer: The probability of getting a queen from a deck of cards is 1 / 13. A frequency distribution describes a specific sample or dataset. Find the probability that the vehicle was a car AND was leased. Solution: The sum of probabilities of all the sample points must equal 1. (a) Find P (R=3 and B=0). Solution: The sample space for rolling 2 dice is given as follows: Thus, the total number of outcomes is 36. 5 calls every hour. Randomness, probability, and simulation Addition rule Multiplication rule for independent events Multiplication rule for dependent events Conditional probability and independence. Problem. The probability of getting an odd and even number is 18 and the probability of getting only odd number is 9. (2) A point is chosen at random on this Flag. These problems and solutions are prepared by our subject experts in accordance with CBSE’s latest syllabus (2023-2024) to help students score better. Example 3: What is the probability that Ram will choose a marble at random and that it is not black if the bowl contains 3 red, 2 black and 5 green marbles. i. Find the percentage of the class that score above and below the given score. 3 (given in the question) Now we will find the probability of e-mail with the word ‘offer’. To find this probability, we need to transform the random variable (p 1 - p 2) into a z-score. If you're curious about the mathematical ins and outs of probability, you've come to the right unit! Here, we'll take a deep dive into the many ways we can calculate the likelihood of different outcomes. William picked two sweets at random. 03. 2. Students can use the NCERT Exemplar for Class 10 Maths for Sep 25, 2020 · 00:45:58 – Find the probability and cumulative probability, expected value, and variance for the binomial distribution (Examples #9-10) 00:59:12 – Find the cumulative probability, expected value, and variance for the binomial distribution (Example #11) Practice Problems with Step-by-Step Solutions ; Chapter Tests with Video Solutions Get NCERT Solutions for Chapter 14 Class 10 free at teachoo. And, consequently, this helps us make better decisions (in the most general sense). 10. 7082 . Game 2: Guess the weight of the man. Simple Probability 1. Define the probability of event (A and B) as the probability of the Probability with discrete random variables. The joint probability formula for independent events is the following: P (A ∩ B) = P (A) * P (B) For example, suppose we have a coin that we flip twice. All Events From the two cases above, we can conclude that the probability of all events fall between 0 and 1. Free practice questions for 7th Grade Math - Probability . P (A): The probability of a customer buying a red shirt is 0. Hence, the least value of n = 4. The probability in the first and the second event is observed to be 1/2 and 1/3 respectively. The words given that clue me into the fact that this is a conditional probability problem. Example 2 Let's repeat the experiment of Example 1, with a die instead of a coin. Simple Probability 2. Probability of a lorry leaving first: c) If either a lorry or van had left first, then there would be 99 vehicles Learn how to calculate probability using formulas and examples. The scores of a midterm are normally distributed with a mean of 85% and a standard deviation of 6%. When you draw five numbers out of 69 without repetition, there are 11,238,513 combinations. Find the probability that the chosen cards are odd-numbered. A continuous random variable can be defined as a Oct 23, 2020 · Example: Finding probability using the z-distribution To find the probability of SAT scores in your sample exceeding 1380, you first find the z-score. a) Score: 91%. The following diagram gives the Binomial Distribution Formula. Classical probability was the first type of probability to be formally studied – partly because it is the simplest, and partly because it was useful for working out how to win at gambling. A dart lands randomly inside the square. Hence, the total number of outcomes for rolling a dice twice is (6x6) = 36. Consider the second insurance example: Probability using combinatorics. Examples and Solutions. See full list on byjus. The shaded area is one unit out of five or 1 / 5 = 20% of the total area. 7 rule from the text. Fill in the probabilities on the branches. No need to wait for office hours or assignments to be graded to find out where you took a wrong turn. Let Y(t) be given by Y(t) = h(t) ∗ X(t), where h(t) is the impulse response of Conditional Probability Questions with Solutions. ⇒ 2 n ≥ 10. Probability is a number between 0 3 examples of the binomial distribution problems and solutions. \ (\dfrac {1} {2} \dfrac {3} {4}\). Some illustrations will improve the understanding of the concept. Determine the likelihood of events with these examples. Probability of a van leaving first: b) Let B be the event of a lorry leaving first. 41) is as follows: Figure 4. The following video explores the normal distribution. Using Stat Trek's Normal Distribution Calculator, we find that the probability of a z-score being -0. Example A Bernoulli random variable is an example of a discrete random variable. Optional Stopping Theorems 9. In Class 11, students also learn the axiomatic approach to probability with suitable examples. In the example below, the distribution ranges from 5 to 10, which covers 5 units. If you roll a six, you win a prize. If you guess within 10 pounds, you win a prize. 6) 3 = 0. Thus, if one story line is randomly selected or generated, the probability that it is about Elvis is 12/ Conditional Probability. We call this conditional probability, and it is governed by the formula that P (A|B) which reads "probability of A given B" is equal to the P (A intersect B)/P (B). Examples: 1. Solution: The total number of possible outcomes of rolling a dice once is 6. E: Basic Concepts of Probability (Exercises) is shared under a CC BY-NC-SA license and was authored, remixed, and/or curated The graph of X ~ B (20, 0. What is the probability that a student is absent given that today is Friday? Solution: Probability is the study of chance or the likelihood of an event happening. Problems with Solutions. Suppose that each pack has probability 0. The additive probability helps, for example, one to find the probability of the values 2 or 5 to be the result of a dice rolling. 8; Thus, using the law of total probability we can calculate the probability of choosing a green Probability with permutations and combinations. If 40% of those who studied got an A, but only 10% of those who don't Jan 8, 2024 · We compute the standard deviation for a probability distribution function the same way that we compute the standard deviation for a sample, except that after squaring \(x - m\), we multiply by \(P(x)\). 7: Probability with Permutations and Combinations is shared under a CC BY 4. Directly or indirectly, probability plays a role in all activities. Learn for free about math, art, computer programming, economics, physics, chemistry Unlike static PDF Introduction to Probability with Texas Hold’em Examples solution manuals or printed answer keys, our experts show you how to solve each problem step-by-step. d. One ball is drawn at random from one of the bags, and it is found to be black. Perhaps the most common real life example of using probability is weather forecasting. Example Question #1 : Probability . Dec 2, 2020 · Probability examples aren’t limited to just mathematics; they’re throughout our daily lives. X is a normally distributed variable with mean μ = 30 and standard deviation σ = 4. Solution: a) Let S be the sample space and A be the event of a van leaving first. In this example, we have the following conditional probabilities: P(G|B 1) = 3/10 = 0. Use the 68-95-99. This video introduces the very basics of Simple Probability, or the likelihood that a single event will occur. What's the probability that we have three 6? What is the probability of getting a queen Sep 19, 2023 · Example 1: Independent Events. Suppose you are running an e-commerce platform, and you want to find the probability of a customer purchasing a red shirt (event A) and a blue hat (event B) independently. From using simulations to the addition and multiplication rules, we'll build a solid foundation that will Simple probability. Let X be the number of students answering yes when 8 students are selected at random and asked the same question. Let’s enter these numbers into the equation: 69 C 5 = 11,238,513. Find the probability that it is the double-tailed coin. OCW is open and available to the world and is a permanent MIT activity Learn the basics of probability theory, such as sample space, favorable outcomes, events, and probability formulas. Mar 26, 2023 · Learn how to define and calculate the probability distribution of a discrete random variable, and how to use it to model real-world situations. Thus it is a Poisson distribution. Updated fornew NCERT Book 2023-2024. Find the probability that the vehicle was a van GIVEN THAT it was used. z p 1 - p 2 = (x - μ p 1 - p 2) / σ d = (0 - 0. 0706 = -0. (ii) Exactly one of them solves the problem. Example 3 A customer help center receives on average 3. Tossing fair coins, rolling dice, and Jun 9, 2022 · A probability distribution is an idealized frequency distribution. What is P (call a person from school) ‍ ?If necessary, round your answer to ‍ decimal places. The probability of the bisection of A and B may be mathematically expressed as p (A ∩ B). Explore different types of events, outcomes, and sample spaces with dice, coins, cards, and more. (b) Complete the diagram to represent the sample space that shows all the possible values of T. Game 1: Roll a die. Example: the probability that a card is a six and black =p (six and black) = 2/52=1/26. For example, “it will probably rain today”, “chances are high that the prices of fuel will go up”, “most probably, Kiran will join the army”, etc. The probability of the student answering yes is 60% = 0. Step 3: Multiply along the branches and add vertically to find the probability of the outcome. e. ‍ of those contacts are people he met at school. The probability that A or B will occur is the sum of The terms p and q remain constant throughout the experiment, where p is the probability of getting a success on any one trial and q = (1 – p) is the probability of getting a failure on any one trial. Two sweets are drawn at random without replacement. Kelly spun a spinner, The NCERT Exemplar Class 10 Maths Chapter 13 Statistics and Probability is provided here for students to prepare for CBSE exams. The probability of an event is a number between 0 and 1 (inclusive). Example 3: Out of 10 people, 3 bought pencils, 5 bought notebooks and 2 got both pencils and notebooks. Let the random variable X be the number of packs of cards Hugo buys. a) What is the probability that it will receive at most 4 calls every hour? b) What is the probability that it will receive at least 5 calls every hour? Solution to Example 3 a) at most 4 calls means no calls, 1 call, 2 calls, 3 calls or 4 calls. The number of times a value occurs in a sample is determined by its probability of occurrence. The random variable T is R multiplied by B. Example 1- Probability Using a Die. Altogether she has 25 balls. Probability is used by weather forecasters to assess how likely it is that there will be rain, snow, clouds, etc. Statisticians refer to these trials as Bernoulli trials. e. Example: A jar consists of 21 sweets. B = Contains the word ‘offer’. Solution: Given, P (A) = Probability of solving the problem by A = 1/2 The card probability = 4 / 52 = 1 / 13. in as per NCERT (CBSE) Guidelines to Score good marks in the board Exams. Alice picks one ball from the bag. To find the probability of pulling a yellow marble from the bag, you need to determine the ratio of the number of yellow marbles to the total number of marbles in the bag. Apr 18, 2019 · Rent 📙Probability 5th edition (978-1108473682) today, or search our site for other 📚textbooks by Rick Durrett. ∴ Total number of pens = 132+12 = 144 pens. A probability tree diagram is a diagram that is used to give a visual representation of the probabilities as well as the outcomes of an event. You either will win or lose a backgammon game. Example: Assume that 75% of the AP Stats students studied for the test. In this case the total is given in the right hand column (22 people). Show Video Lesson. Feb 18, 2021 · Instead we need to use the conditional probability of G, given some events B where the B i ‘s form a partition of the sample space S. 1) 6. 2 of containing the card Hugo is hoping for. In Class 9, we studied about Empirical or Experimental Probability. Unit 7: Probability. So, the number of favourable outcomes = 4. Conditional Expectation 2. 3; P(G|B 2) = 8/10 = 0. Martingales, Almost Sure Convergence 3. ⇒(1/2) n ≤ 0. Probability solutions are updated as per Example 1: Suppose a pair of fair dice are rolled. 41) = 8. Question 1: The probability that it is Friday and that a student is absent is 0. Includes full solutions and score reporting. The speeds are normally distributed with a mean of 90 km/hr and a standard deviation of 10 km/hr. 1 and the probability the second bus will be late is 0. n ( A) = 30. If both try to solve the problem independently, find the probability that (i) The problem is solved. Forecasters will regularly say things like “there is an 80% chance of rain Probability of picking 2 green balls and 1 blue ball = 4/14 * 3/13 * 5/12 = 5/182. Therefore, the probability of each sample point (heads or tails) must be equal to 1/2. Solution. Square Integrable Martingales (was Subsection 5. 00:39:39 – Find the probabilities for the exponential distribution (Examples #4-5) Classical probability is the name we give to probability where there are a finite number of equally likely outcomes. A discrete probability distribution function has two characteristics: Each probability is between zero and one, inclusive. Example Questions Using Probability Formulas. Solution: The probability of defective units p = 3/100 = 0. MIT OpenCourseWare is a web based publication of virtually all MIT course content. The condition is that I know that the dice came up an even Jul 29, 2020 · Solution with Bayes’ Equation: A = Spam. A probability tree diagram consists of two parts - nodes and branches. Theoretical Probability, that is, P (E) = Number of outcomes with E / Total possible Example 2: - A magician takes out two cards from a deck of cards, one after the other, without replacement. Addition Rule 1: When two events, A and B, are mutually exclusive, the probability that A or B will occur is the sum of the probability of each event. Of those 21 possible story lines, 12 were about Elvis. 1. 95) whereas the probability that he plays given that it is a rainy day is less which is 10% (0. Find the probability that in a sample of 200 units, less than 2 bulbs are defective. yt ry fd vu ni yi iy nl po dw