C Solved Programs Ebook Download' title='C Solved Programs Ebook Download' />Probability Theory, solved examples and practice questions. When MS and MBA applicants ask us What are my chances of getting into Harvard or Whats my probability of getting scholarships from Oxford we get tongue tied. There are so many variables at play, its difficult to give an accurate answer. But when you get probability questions in your GMAT exam syllabus, you dont have to get flummoxed. Understanding the basic rules and formulas of probability will help you score high in the entrance exams. Meaning and definition of Probability. Game Plants Vs Zombie Untuk Pc. As the Oxford dictionary states it, Probability means The extent to which something is probable the likelihood of something happening or being the case. In mathematics too, probability indicates the same the likelihood of the occurrence of an event. Examples of events can be Tossing a coin with the head up. Drawing a red pen from a pack of different coloured pens. Drawing a card from a deck of 5. Either an event will occur for sure, or not occur at all. Nodal Analysis Introduction Nodal analysis is a systematic method to determine the voltage at each node relative to the reference node by repeatedly ap. Online homework and grading tools for instructors and students that reinforce student learning through practice and instant feedback. How to solve probability questions in GMAT math sections. All about probability meaning, definition, theory, formulas and examples. Corporate eLibrary Discover our employee learning solutions This is a Premium eBook Bookboon Premium Gain access to over 800 eBooks without ads. Quickly Analyze Apartment Building Deals with the Syndicated Deal Analyzer Stop Spending Hours Analyzing your Commercial Real Estate Deals Analyze Deals and Make. Rense. com is the single most important news aggregate site on the internet. The spectrum of stories, ideas and revelations presented, on a. Or there are possibilities to different degrees the event may occur. An event that occurs for sure is called a Certain event and its probability is 1. GQ5/9780273769385.jpg' alt='C Solved Programs Ebook Download' title='C Solved Programs Ebook Download' />An event that doesnt occur at all is called an impossible event and its probability is 0. This means that all other possibilities of an event occurrence lie between 0 and 1. This is depicted as follows 0 lt PA lt 1where A is an event and PA is the probability of the occurrence of the event. This also means that a probability value can never be negative. Every event will have a set of possible outcomes. I am here today to redownload Marks free eBook template. It gets buried in my files so deeply that its easier to come here for a redownload. Writing ebooks that actually sell means you have to solve a certain kind of problem. This article explains what kind. Download the free trial version below to get started. Doubleclick the downloaded file to install the software. It is called the sample space. Consider the example of tossing a coin. When a coin is tossed, the possible outcomes are Head and Tail. So, the sample space is represented as H, T. Similarly when two coins are tossed, the sample space is H,H, H,T, T,H, T,T. The probability of head each time you toss the coin is 12. So is the probability of tail. Basic formula of probability. As you might know from the list of GMAT maths formulas, the Probability of the occurrence of an event A is defined as PA No. A can occurTotal no. Another example is the rolling of dice. When a single die is rolled, the sample space is 1,2,3,4,5,6. What is the probability of rolling a 5 when a die is rolled No. Total no. of possible outcomes 6. So the probability of rolling a particular number when a die is rolled 16. Compound probability. Compound probability is when the problem statement asks for the likelihood of the occurrence of more than one outcome. Formula for compound probability. PA or B PA PB PA and Bwhere A and B are any two events. PA or B is the probability of the occurrence of atleast one of the events. PA and B is the probability of the occurrence of both A and B at the same time. Mutually exclusive events Mutually exclusive events are those where the occurrence of one indicates the non occurrence of the other. ORWhen two events cannot occur at the same time, they are considered mutually exclusive. Note For a mutually exclusive event, PA and B 0. Example 1 What is the probability of getting a 2 or a 5 when a die is rolledSolution Taking the individual probabilities of each number, getting a 2 is 16 and so is getting a 5. Applying the formula of compound probability,Probability of getting a 2 or a 5,P2 or 5 P2 P5 P2 and 5      16 16 0      26 13. Example 2 Consider the example of finding the probability of selecting a black card or a 6 from a deck of 5. Solution We need to find out PB or 6Probability of selecting a black card  2. Probability of selecting a 6                 45. Probability of selecting both a black card and a 6 25. PB or 6          PB P6 PB and 6 2. Independent and Dependent Events. Independent Event. When multiple events occur, if the outcome of one event DOES NOT affect the outcome of the other events, they are called independent events. Say, a die is rolled twice. The outcome of the first roll doesnt affect the second outcome. These two are independent events. Example 1 Say, a coin is tossed twice. What is the probability of getting two consecutive tails Probability of getting a tail in one toss 12. The coin is tossed twice. So 12 12 14 is the answer. Heres the verification of the above answer with the help of sample space. When a coin is tossed twice, the sample space is H,H, H,T, T,H, T,T. Our desired event is T,T whose occurrence is only once out of four possible outcomes and hence, our answer is 14. Example 2 Consider another example where a pack contains 4 blue, 2 red and 3 black pens. If a pen is drawn at random from the pack, replaced and the process repeated 2 more times, What is the probability of drawing 2 blue pens and 1 black pen Solution. Here, total number of pens 9. Probability of drawing 1 blue pen 49. Probability of drawing another blue pen 49. Probability of drawing 1 black pen 39. Probability of drawing 2 blue pens and 1 black pen 49 49 39 88. Dependent Events. When two events occur, if the outcome of one event affects the outcome of the other, they are called dependent events. Consider the aforementioned example of drawing a pen from a pack, with a slight difference. Example 1 A pack contains 4 blue, 2 red and 3 black pens. If 2 pens are drawn at random from the pack, NOT replaced and then another pen is drawn. What is the probability of drawing 2 blue pens and 1 black pen Solution Probability of drawing 1 blue pen 49. Probability of drawing another blue pen 38. Probability of drawing 1 black pen 37. Probability of drawing 2 blue pens and 1 black pen 49 38 37 11. Lets consider another example Example 2 What is the probability of drawing a king and a queen consecutively from a deck of 5. Probability of drawing a king 45. After drawing one card, the number of cards are 5. Probability of drawing a queen 45. Now, the probability of drawing a king and queen consecutively is 11. Conditional probability. Conditional probability is calculating the probability of an event given that another event has already occured. The formula for conditional probability PAB, read as PA given B is. PAB P A and B PBConsider the following example Example In a class, 4. What is the probability of a student studying science given heshe is already studying mathSolution. PM and S 0. PM 0. PSM PM and SPS 0. Complement of an event. A complement of an event A can be stated as that which does NOT contain the occurrence of A. A complement of an event is denoted as PAc or PA. PAc 1 PAor it can be stated, PAPAc 1. For example,if A is the event of getting a head in coin toss, Ac is not getting a head i. A is the event of getting an even number in a die roll, Ac is the event of NOT getting an even number i. A is the event of randomly choosing a number in the range of 3 to 3, Ac is the event of choosing every number that is NOT negative i. Consider the following example Example A single coin is tossed 5 times. What is the probability of getting at least one head Solution Consider solving this using complement. Probability of getting no head Pall tails 13. Pat least one head 1 Pall tails 1 13. Sample Probability questions with solutions. Probability Example 1. What is the probability of the occurrence of a number that is odd or less than 5 when a fair die is rolled. 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