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Explains how to compute probabilities using counting and relative frequency, including worked examples with dice, cards, and coin tossing. Introduces the language of probability through sets, sample spaces, and events, including definitions of sets, elements, subsets, and the empty set, with emphasis on well-defined probability experiments and proper outcome specification.",{"@graph":69,"@context":122},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":20,"@type":76,"position":81},"https://docshare.wps.com/document/exam/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/study-notes-general-probability/399235/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/study-notes-general-probability/399235.png","ImageObject",300,407,{"name":92,"@type":93},"Anna Hans","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-28","2026-09-27",true,{"@type":102,"interactionType":103,"userInteractionCount":39},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"How is probability defined in these notes?","Question",{"text":112,"@type":113},"Probability is defined as a set function over a collection of events, with probability values between 0 and 1. The notes also state the basic axioms of probability.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"What methods are used to determine probabilities?",{"text":117,"@type":113},"The notes describe two main methods: counting outcomes and relative frequency from experiments or trials. Each method leads to a probability estimate using favorable outcomes.",{"name":119,"@type":110,"acceptedAnswer":120},"Why must a probability experiment have all outcomes specified?",{"text":121,"@type":113},"Outcomes must be fully identified so the experiment is well-defined and so the probability can be computed correctly from the sample space. 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Reproduction and/or distribution of this document is prohibited. Infringers will be prosecuted in their local jurisdictions .”  \nTable of Contents  \nDefine set functions, Venn diagrams, sample space, and events.  \n1 - Define probability as a set function on a collection of events and state the basic axioms of probability.  \nCalculate probabilities using the addition and multiplication 2 -  \nrules.  \nDefine independence and calculate probability of independent  \n3 -events.  \n4 - Calculate probabilities of mutually exclusive events.  \n5 - Define and calculate conditional probabilities.  \nCalculate probabilities using combinatorics, such as 6 -  \ncombinations and permutations.  \nState Bayes Theorem and use it to calculate conditional 7 -  \nprobabilities.  \n3  \n17  \n24  \n27  \n30  \n33  \n40  \n2  \n© 2014-2023 AnalystPrep.  \nReading 1: Define set functions, Venn diagrams, sample space, and events . Define probability as a set function on a collection of events and state the basic axioms of probability.  \n1. What Is Probability?  \nIn mathematics, probability is the branch that deals with numerical descriptions of the likelihood that events will occur or that propositions are true. Probability is a number between 0 and 1, with 0 representing impossibility and 1 representing certitude (certainty) . The higher the probability of an event, the more likely it is that the event will occur. Probabilities can be determined via two methods: counting and relative frequency.  \nCounting  \nCounting can be used to estimate probabilities in a wide variety of situations. For example, counting is used to solve problems in gambling that involves dice and cards. For example, let’s say you’re rolling a fair six-sided die labeled 1, 2, 3, 4, 5, and 6. The probability that you will roll a number less than 4 is 3/6 since there are three outcomes that are less than 4 (1,2, and 3) and there are six possible and equally likely outcomes. The probability approach used in this approach is summarized as follows:  \nNumber of favorable outcomes  \nProbability of event, P (E) = Total Number of outcomes  \nQuestion 1. 1  \nThere are 12 pillows in a bed, 5 are white, 3 are green, 2 are yellow, and 2 are blue. What is the probability of picking a white pillow?  \nSolution  \nThe probability is equal to the number of white pillows in the bed divided by the total number of pillows, i.e., 5/12  \nRelative Frequency  \n3  \n© 2014-2023 AnalystPrep.  \nA relative frequency probability is found on the basis of experiments or trials. When examining the relative frequency of an event during an experiment, we consider how many times the event occurs as a proportion of the total number of trials:  \nNumber of favorable outcomes in n trials  \nProbability of event, P (E) =  n   \nFor example, let’s say you’re tossing a fair coin. In this case, you cannot determine the probability of tossing a tail by counting. However, you can estimate the probability by tossing the coin a large number of times and then count the number of tails. If you toss the coin 1000 times and observe 550 tails, your best estimate of the probability of a tail on one toss is 550/1000 or 0.55.  \nQuestion 1.2  \nJames asks some people in his town about their dietary preferences and records the results  \nin the table below:  \n\n| Dietary Preference | Frequency |\n| --- | --- |\n| Vegetarian | 60 |\n| Vegan | 30 |\n| Other | 60 |\n\nWhat’s the relative frequency of someone in the town being vegetarian? If there are 10,000 people in James’ town, find an estimate for the number of people in this town who are vegetarian.  \nSolution  \nFirstly, we need the total number of trials:  \ntrials = 60 + 30 + 60 = 150  \nNow, using the formula above,  \nRelative frequency = 60150 = 410 or 0.4  \nOur Solution suggests that if we picked someone from James’ t","cbCaijXpQTpTSDk0","https://ap.wps.com/l/cbCaijXpQTpTSDk0","pdf",875384,44,"English","# Table of Contents\n## Define probability as a set function; axioms of probability\n## Calculate probabilities using addition and multiplication rules\n## Independence and probability of independent events\n## Mutually exclusive events\n## Conditional probabilities\n## Combinatorics: combinations and permutations\n## Bayes Theorem and conditional probabilities","[{\"question\":\"How is probability defined in these notes?\",\"answer\":\"Probability is defined as a set function over a collection of events, with probability values between 0 and 1. The notes also state the basic axioms of probability.\"},{\"question\":\"What methods are used to determine probabilities?\",\"answer\":\"The notes describe two main methods: counting outcomes and relative frequency from experiments or trials. Each method leads to a probability estimate using favorable outcomes.\"},{\"question\":\"Why must a probability experiment have all outcomes specified?\",\"answer\":\"Outcomes must be fully identified so the experiment is well-defined and so the probability can be computed correctly from the sample space. Otherwise, an analyst may not know which outcomes are possible.\"}]","Study Notes - General Probability | PDF",1790495092,111]