{"id":403,"date":"2019-08-17T13:28:00","date_gmt":"2019-08-17T13:28:00","guid":{"rendered":"https:\/\/analystprep.com\/cfa-level-1-exam\/?p=403"},"modified":"2025-12-30T13:39:00","modified_gmt":"2025-12-30T13:39:00","slug":"introduction-probability-defining-basic-terms","status":"publish","type":"post","link":"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/introduction-probability-defining-basic-terms\/","title":{"rendered":"Introduction to Probability: Definition of Terms"},"content":{"rendered":"\n<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"VideoObject\",\n  \"name\": \"Probability Concepts (2021 Level I CFA\u00ae Exam \u2013 Reading 8)\",\n  \"description\": \"This CFA Level I lecture on Probability Concepts covers fundamental statistical tools like random variables, probability rules, conditional expectations, Bayes' theorem, and portfolio variance. It explains event classification, tree diagrams, combinations, permutations, and covariance\/correlation, using finance-focused examples to reinforce concepts essential for quantitative analysis in investment decision-making.\",\n  \"uploadDate\": \"2020-10-01T00:00:00+00:00\",\n  \"thumbnailUrl\": \"https:\/\/i.ytimg.com\/vi\/hu47ZbsskEw\/hqdefault.jpg\",\n  \"contentUrl\": \"https:\/\/www.youtube.com\/watch?v=hu47ZbsskEw\",\n  \"embedUrl\": \"https:\/\/www.youtube.com\/embed\/hu47ZbsskEw\",\n  \"duration\": \"PT48M33S\"\n}\n<\/script>\n\n\n\n<iframe loading=\"lazy\" width=\"560\" height=\"315\" src=\"https:\/\/www.youtube.com\/embed\/hu47ZbsskEw?si=uqATHhK5etK3-RYf\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\n\n\n\n\n<p>Probability is a measure of the likelihood that something will happen. We usually express probabilities as percentages, from 0 (impossible to happen) to 100% (guaranteed). In fact, we can express almost any event as a probability, e.g., the likelihood that it will rain on a given day or the likelihood of one passing an examination.<\/p>\n<p>Estimation of probabilities is imperative in financial management. More precisely, concepts in probability help analysts <strong>quantify risks<\/strong>. The following are the major probability concepts you should know.<\/p>\n<p><!--more--><\/p>\n<h2><strong>Random Variable<\/strong><\/h2>\n<p>A random variable is any quantity whose expected future value is not known in advance. Examples include the expected <a href=\"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/time-value-money-explained-example\/\">future value<\/a> of a mutual fund, expected dividend payment on a stock, or the expected <a href=\"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/measures-dispersion-examples\/\">standard deviation<\/a> of investment returns. We cannot know the exact future value of an investment since it is usually a function of multiple factors, some of which may be beyond the control of the financial manager.<\/p>\n<p>Note that returns that are fixed cannot be described as random variables. For instance, if a government bond is quoted at a fixed discount of, say, 6%, the bond\u2019s future value can be calculated in advance. Therefore, it is not a random variable.<\/p>\n<h2><strong>Outcome<\/strong><\/h2>\n<p>An outcome is any possible value that a random variable can take. For example, if you roll a six-sided dice, there are six possible outcomes since any number, from 1 to 6, can come up.<\/p>\n<p>If, for example, 3 comes up, then that is an outcome. In case 5 comes up, it\u2019s another outcome. So, for example, if a stock offers shareholders a $2 dividend per share at the end of a year, then the $2 dividend is an outcome.<\/p>\n<h2><strong>Event<\/strong><\/h2>\n<p>A single outcome or a set of outcomes is known as an event. If we take the dice example above, rolling a 4 is an event, rolling an odd number.<\/p>\n<h2><strong>Mutually Exclusive Events<\/strong><\/h2>\n<p>Mutually exclusive events are such that one event precludes the occurrence of all the other events. Thus, if you roll a dice and a 4 comes up, that particular event precludes all the other events, i.e., 1, 2, 3, 5, and 6. In other words, rolling a 1 and a 5 are mutually exclusive events: they cannot occur simultaneously.<\/p>\n<p>Furthermore, there is no way a single investment can have more than one arithmetic mean return. Therefore, arithmetic returns of, say, 20% and 17% constitute mutually exclusive events.<\/p>\n<h2><strong>Exhaustive Events<\/strong><\/h2>\n<p>Events are said to be exhaustive if they include all possible outcomes. Suppose we roll a dice once and categorize the outcomes into two events as follows:<\/p>\n<p>{1, 3, 5}\u00a0\u00a0 {2, 4, 6}<\/p>\n<p>Each of the above set of outcomes is an event. The two events are exhaustive because they include all the possible outcomes.<\/p>\n<div class=\"notes_inv\"><hr \/>\n<p><a href=\"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/learning-sessions-curriculum\/\"><em>s<\/em><\/a><\/p>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>Probability is a measure of the likelihood that something will happen. We usually express probabilities as percentages, from 0 (impossible to happen) to 100% (guaranteed). In fact, we can express almost any event as a probability, e.g., the likelihood that&#8230;<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[2],"tags":[],"class_list":["post-403","post","type-post","status-publish","format-standard","hentry","category-quantitative-methods","blog-post","no-post-thumbnail","animate"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.9 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Basic Probability Terms Explained | CFA Level 1<\/title>\n<meta name=\"description\" content=\"Learn key probability terms used in CFA exams. 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