{"id":349,"date":"2016-10-11T19:51:15","date_gmt":"2016-10-11T19:51:15","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/math4libarts\/?post_type=chapter&#038;p=349"},"modified":"2017-04-04T23:30:49","modified_gmt":"2017-04-04T23:30:49","slug":"calculating-the-odds-of-an-event","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/wm-mathforliberalarts\/chapter\/calculating-the-odds-of-an-event\/","title":{"raw":"Why It Matters: Probability","rendered":"Why It Matters: Probability"},"content":{"raw":"According to the news, the lottery jackpot is climbing by the hour. \u00a0Long lines of dreamers are forming wherever lottery tickets are sold. \u00a0While you don\u2019t usually buy lottery tickets, it is getting tempting. \u00a0Just imagine what you could do with $100 million dollars. \u00a0Perhaps you could retire early or never even go to work. \u00a0Maybe buy a rare fancy car. \u00a0All you need to do is pick the correct numbers, and the jackpot is all yours!\r\n\r\n<a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/03\/29202931\/01-bonhams-ferrari-monterey-2014-1.jpg\"><img class=\"wp-image-2411 aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/03\/29202931\/01-bonhams-ferrari-monterey-2014-1-300x169.jpg\" alt=\"Image of a red Ferrari 250 GTO on a display platform.\" width=\"460\" height=\"259\" \/><\/a>\r\n\r\nIt sounds easy enough; just six simple numbers. \u00a0But how likely are you to win? \u00a0And could you increase the likelihood of winning by purchasing more lottery tickets?\r\n<p style=\"text-align: center;\"><a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/03\/29203238\/lotto-balls.jpg\"><img class=\"wp-image-2412 aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/03\/29203238\/lotto-balls-300x298.jpg\" alt=\"Image shows numbered balls as would be used to select the winning numbers of a lottery.\" width=\"220\" height=\"218\" \/><\/a><\/p>\r\nTo answer these questions, you need to know about permutations and combinations. \u00a0So learn about them as you complete this module, and then we\u2019ll return to the lottery at the end. \u00a0Then you\u2019ll be able to decide whether you want to stand in line to purchase a ticket.\r\n\r\n&nbsp;\r\n<div class=\"textbox learning-objectives\">\r\n<h3>Learning Objectives<\/h3>\r\n<div id=\"post-1384\" class=\"miscellaneous post-1384 front-matter type-front-matter status-publish hentry\">\r\n<div class=\"entry-content\">\r\n\r\nComputing the Probability of an Event\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\nApplications With Probability\r\n<ul>\r\n \t<li>Compute a conditional probability for an event<\/li>\r\n \t<li>Use Baye\u2019s theorem to compute a conditional probability<\/li>\r\n \t<li>Calculate the expected value of an event<\/li>\r\n<\/ul>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n&nbsp;","rendered":"<p>According to the news, the lottery jackpot is climbing by the hour. \u00a0Long lines of dreamers are forming wherever lottery tickets are sold. \u00a0While you don\u2019t usually buy lottery tickets, it is getting tempting. \u00a0Just imagine what you could do with $100 million dollars. \u00a0Perhaps you could retire early or never even go to work. \u00a0Maybe buy a rare fancy car. \u00a0All you need to do is pick the correct numbers, and the jackpot is all yours!<\/p>\n<p><a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/03\/29202931\/01-bonhams-ferrari-monterey-2014-1.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-2411 aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/03\/29202931\/01-bonhams-ferrari-monterey-2014-1-300x169.jpg\" alt=\"Image of a red Ferrari 250 GTO on a display platform.\" width=\"460\" height=\"259\" \/><\/a><\/p>\n<p>It sounds easy enough; just six simple numbers. \u00a0But how likely are you to win? \u00a0And could you increase the likelihood of winning by purchasing more lottery tickets?<\/p>\n<p style=\"text-align: center;\"><a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/03\/29203238\/lotto-balls.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-2412 aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/03\/29203238\/lotto-balls-300x298.jpg\" alt=\"Image shows numbered balls as would be used to select the winning numbers of a lottery.\" width=\"220\" height=\"218\" \/><\/a><\/p>\n<p>To answer these questions, you need to know about permutations and combinations. \u00a0So learn about them as you complete this module, and then we\u2019ll return to the lottery at the end. \u00a0Then you\u2019ll be able to decide whether you want to stand in line to purchase a ticket.<\/p>\n<p>&nbsp;<\/p>\n<div class=\"textbox learning-objectives\">\n<h3>Learning Objectives<\/h3>\n<div id=\"post-1384\" class=\"miscellaneous post-1384 front-matter type-front-matter status-publish hentry\">\n<div class=\"entry-content\">\n<p>Computing the Probability of an Event<\/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<p>Applications With Probability<\/p>\n<ul>\n<li>Compute a conditional probability for an event<\/li>\n<li>Use Baye\u2019s theorem to compute a conditional probability<\/li>\n<li>Calculate the expected value of an event<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/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-349\">\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>Why It Matters: Probability. <strong>Authored 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\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Ferrari 250 GTO. <strong>Authored by<\/strong>: Aekkm. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/commons.wikimedia.org\/wiki\/File:01-bonhams-ferrari-monterey-2014-1.jpg\">https:\/\/commons.wikimedia.org\/wiki\/File:01-bonhams-ferrari-monterey-2014-1.jpg<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by-sa\/4.0\/\">CC BY-SA: Attribution-ShareAlike<\/a><\/em><\/li><li>Lotto Balls. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/pixabay.com\/en\/lotto-balls-gambling-lottery-864035\">https:\/\/pixabay.com\/en\/lotto-balls-gambling-lottery-864035<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/about\/cc0\">CC0: No Rights Reserved<\/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":20,"menu_order":1,"template":"","meta":{"_candela_citation":"[{\"type\":\"original\",\"description\":\"Why It Matters: Probability\",\"author\":\"Lumen Learning\",\"organization\":\"\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Ferrari 250 GTO\",\"author\":\"Aekkm\",\"organization\":\"\",\"url\":\"https:\/\/commons.wikimedia.org\/wiki\/File:01-bonhams-ferrari-monterey-2014-1.jpg\",\"project\":\"\",\"license\":\"cc-by-sa\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Lotto Balls\",\"author\":\"\",\"organization\":\"\",\"url\":\"https:\/\/pixabay.com\/en\/lotto-balls-gambling-lottery-864035\",\"project\":\"\",\"license\":\"cc0\",\"license_terms\":\"\"}]","CANDELA_OUTCOMES_GUID":"bcc9ceed-19f6-4ca5-a540-ed5a5c1eb03c","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-349","chapter","type-chapter","status-publish","hentry"],"part":329,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/wm-mathforliberalarts\/wp-json\/pressbooks\/v2\/chapters\/349","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/wm-mathforliberalarts\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/wm-mathforliberalarts\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-mathforliberalarts\/wp-json\/wp\/v2\/users\/20"}],"version-history":[{"count":10,"href":"https:\/\/courses.lumenlearning.com\/wm-mathforliberalarts\/wp-json\/pressbooks\/v2\/chapters\/349\/revisions"}],"predecessor-version":[{"id":2413,"href":"https:\/\/courses.lumenlearning.com\/wm-mathforliberalarts\/wp-json\/pressbooks\/v2\/chapters\/349\/revisions\/2413"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/wm-mathforliberalarts\/wp-json\/pressbooks\/v2\/parts\/329"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/wm-mathforliberalarts\/wp-json\/pressbooks\/v2\/chapters\/349\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/wm-mathforliberalarts\/wp-json\/wp\/v2\/media?parent=349"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-mathforliberalarts\/wp-json\/pressbooks\/v2\/chapter-type?post=349"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-mathforliberalarts\/wp-json\/wp\/v2\/contributor?post=349"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-mathforliberalarts\/wp-json\/wp\/v2\/license?post=349"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}