{"id":1257,"date":"2017-02-01T22:10:20","date_gmt":"2017-02-01T22:10:20","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/waymakermath4libarts\/?post_type=chapter&#038;p=1257"},"modified":"2017-04-18T20:17:51","modified_gmt":"2017-04-18T20:17:51","slug":"computing-the-probability-of-an-event","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/wm-mathforliberalarts\/chapter\/computing-the-probability-of-an-event\/","title":{"raw":"Introduction: Computing the Probability of an Event","rendered":"Introduction: Computing the Probability of an Event"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Objectives<\/h3>\r\nThe learning outcomes for this section include:\r\n<ul>\r\n \t<li>Describe a sample space and simple and compound events in it using standard notation<\/li>\r\n \t<li>Calculate the probability of an event using standard notation<\/li>\r\n \t<li>Calculate the probability of two independent events using standard notation<\/li>\r\n \t<li>Recognize when two events are mutually exclusive<\/li>\r\n \t<li>Calculate a conditional probability using standard notation<\/li>\r\n<\/ul>\r\n<\/div>\r\nProbability is the likelihood of a particular outcome or event happening. Statisticians and actuaries use probability to make predictions about events. \u00a0An actuary that works for a car insurance company would, for example, be interested in how likely a 17 year old male would be to get in a car accident. \u00a0They would use data from past events to make predictions about future events using the characteristics of probabilities, then use this information to calculate an insurance rate.\r\n\r\nIn this section, we will explore the definition of an event, and learn how to calculate the probability of it's occurance. \u00a0We will also practice using standard mathematical notation to calculate and describe different kinds of probabilities.\r\n\r\n<a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/02\/01222858\/Car_crash_1.jpg\"><img class=\"wp-image-1263 aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/02\/01222858\/Car_crash_1-300x225.jpg\" alt=\"\" width=\"613\" height=\"462\" \/><\/a>\r\n","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Objectives<\/h3>\n<p>The learning outcomes for this section include:<\/p>\n<ul>\n<li>Describe a sample space and simple and compound events in it using standard notation<\/li>\n<li>Calculate the probability of an event using standard notation<\/li>\n<li>Calculate the probability of two independent events using standard notation<\/li>\n<li>Recognize when two events are mutually exclusive<\/li>\n<li>Calculate a conditional probability using standard notation<\/li>\n<\/ul>\n<\/div>\n<p>Probability is the likelihood of a particular outcome or event happening. Statisticians and actuaries use probability to make predictions about events. \u00a0An actuary that works for a car insurance company would, for example, be interested in how likely a 17 year old male would be to get in a car accident. \u00a0They would use data from past events to make predictions about future events using the characteristics of probabilities, then use this information to calculate an insurance rate.<\/p>\n<p>In this section, we will explore the definition of an event, and learn how to calculate the probability of it&#8217;s occurance. \u00a0We will also practice using standard mathematical notation to calculate and describe different kinds of probabilities.<\/p>\n<p><a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/02\/01222858\/Car_crash_1.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-1263 aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/02\/01222858\/Car_crash_1-300x225.jpg\" alt=\"\" width=\"613\" height=\"462\" \/><\/a><\/p>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-1257\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Original<\/div><ul class=\"citation-list\"><li>Introduction and outcomes. <strong>Provided by<\/strong>: Lumen Learning. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">Public domain content<\/div><ul class=\"citation-list\"><li> A car crash on Jagtvej, a road in Copenhagen, Denmark. <strong>Authored by<\/strong>: By Thue (Own work) . <strong>Provided by<\/strong>: Wikimedia Commons. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/commons.wikimedia.org\/wiki\/File%3ACar_crash_1.jpg,%20https:\/\/upload.wikimedia.org\/wikipedia\/commons\/e\/e1\/Car_crash_1.jpg\">https:\/\/commons.wikimedia.org\/wiki\/File%3ACar_crash_1.jpg,%20https:\/\/upload.wikimedia.org\/wikipedia\/commons\/e\/e1\/Car_crash_1.jpg<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/about\/pdm\">Public Domain: No Known Copyright<\/a><\/em><\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":21,"menu_order":2,"template":"","meta":{"_candela_citation":"[{\"type\":\"pd\",\"description\":\" A car crash on Jagtvej, a road in Copenhagen, Denmark\",\"author\":\"By Thue (Own work) \",\"organization\":\"Wikimedia Commons\",\"url\":\"https:\/\/commons.wikimedia.org\/wiki\/File%3ACar_crash_1.jpg, https:\/\/upload.wikimedia.org\/wikipedia\/commons\/e\/e1\/Car_crash_1.jpg\",\"project\":\"\",\"license\":\"pd\",\"license_terms\":\"\"},{\"type\":\"original\",\"description\":\"Introduction and outcomes\",\"author\":\"\",\"organization\":\"Lumen 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