{"id":79,"date":"2023-01-25T16:34:02","date_gmt":"2023-01-25T16:34:02","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/chapter\/computing-the-probability-of-an-event-learn-it-page-1\/"},"modified":"2024-03-22T18:16:21","modified_gmt":"2024-03-22T18:16:21","slug":"computing-the-probability-of-an-event-learn-it-1","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/chapter\/computing-the-probability-of-an-event-learn-it-1\/","title":{"raw":"Computing the Probability of an Event: Learn It 1","rendered":"Computing the Probability of an Event: Learn It 1"},"content":{"raw":"<section class=\"textbox learningGoals\">\r\n<ul>\r\n\t<li>Describe events in a sample space<\/li>\r\n\t<li>Calculate the probability of different types of events<\/li>\r\n\t<li>Find the conditional probability of an event<\/li>\r\n<\/ul>\r\n<\/section>\r\n<section class=\"textbox proTip\">You've seen before that learning mathematics is similar to learning a new language -- it takes repetition and practice to obtain new vocabulary and symbols. Probability is no different. The set of vocabulary and symbols used in probability will likely be completely unfamiliar to you unless you've studied probability before. Remember to read the text with your pencil, write out the terms, definitions, and practice problems multiple times in order to learn them. You'll need to spend time with these new ways of thinking to make them your own.<\/section>\r\n\r\nUnderstanding probability involves grasping the concepts of events and outcomes within the framework of experiments. These fundamental ideas help us quantify the likelihood of various occurrences and are crucial for making predictions based on statistical evidence.\r\n\r\n<section class=\"textbox keyTakeaway\">\r\n<div>\r\n<h3>events and outcomes<\/h3>\r\n<ul>\r\n\t<li>The result of an experiment is called an <strong>outcome<\/strong>.<\/li>\r\n\t<li>An <strong>event<\/strong> is any particular outcome or group of outcomes.<\/li>\r\n\t<li>A <strong>simple event <\/strong>is an event that cannot be broken down further<\/li>\r\n\t<li>A <strong>compound event <\/strong>is a combination of two or more simple events<\/li>\r\n\t<li>The <strong>sample space<\/strong> is the set of all possible simple events.<\/li>\r\n<\/ul>\r\n<\/div>\r\n<\/section>\r\n<section class=\"textbox seeExample\">If we roll a standard [latex]6[\/latex]-sided die, describe the sample space and some simple events.[reveal-answer q=\"997648\"]Show Solution[\/reveal-answer]<br \/>\r\n[hidden-answer a=\"997648\"]The sample space is the set of all possible simple events: [latex]{1,2,3,4,5,6}[\/latex]. Some examples of simple events:\r\n\r\n\r\n<ul>\r\n\t<li>We roll a [latex]1[\/latex]<\/li>\r\n\t<li>We roll a [latex]5[\/latex]<\/li>\r\n<\/ul>\r\n<p>Some compound events:<\/p>\r\n<ul>\r\n\t<li>We roll a number bigger than [latex]4[\/latex]<\/li>\r\n\t<li>We roll an even number<\/li>\r\n<\/ul>\r\n<p>[\/hidden-answer]<\/p>\r\n<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]2807[\/ohm2_question]<\/section>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li>Describe events in a sample space<\/li>\n<li>Calculate the probability of different types of events<\/li>\n<li>Find the conditional probability of an event<\/li>\n<\/ul>\n<\/section>\n<section class=\"textbox proTip\">You&#8217;ve seen before that learning mathematics is similar to learning a new language &#8212; it takes repetition and practice to obtain new vocabulary and symbols. Probability is no different. The set of vocabulary and symbols used in probability will likely be completely unfamiliar to you unless you&#8217;ve studied probability before. Remember to read the text with your pencil, write out the terms, definitions, and practice problems multiple times in order to learn them. You&#8217;ll need to spend time with these new ways of thinking to make them your own.<\/section>\n<p>Understanding probability involves grasping the concepts of events and outcomes within the framework of experiments. These fundamental ideas help us quantify the likelihood of various occurrences and are crucial for making predictions based on statistical evidence.<\/p>\n<section class=\"textbox keyTakeaway\">\n<div>\n<h3>events and outcomes<\/h3>\n<ul>\n<li>The result of an experiment is called an <strong>outcome<\/strong>.<\/li>\n<li>An <strong>event<\/strong> is any particular outcome or group of outcomes.<\/li>\n<li>A <strong>simple event <\/strong>is an event that cannot be broken down further<\/li>\n<li>A <strong>compound event <\/strong>is a combination of two or more simple events<\/li>\n<li>The <strong>sample space<\/strong> is the set of all possible simple events.<\/li>\n<\/ul>\n<\/div>\n<\/section>\n<section class=\"textbox seeExample\">If we roll a standard [latex]6[\/latex]-sided die, describe the sample space and some simple events.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q997648\">Show Solution<\/button><\/p>\n<div id=\"q997648\" class=\"hidden-answer\" style=\"display: none\">The sample space is the set of all possible simple events: [latex]{1,2,3,4,5,6}[\/latex]. Some examples of simple events:<\/p>\n<ul>\n<li>We roll a [latex]1[\/latex]<\/li>\n<li>We roll a [latex]5[\/latex]<\/li>\n<\/ul>\n<p>Some compound events:<\/p>\n<ul>\n<li>We roll a number bigger than [latex]4[\/latex]<\/li>\n<li>We roll an even number<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm2807\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=2807&theme=lumen&iframe_resize_id=ohm2807&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n","protected":false},"author":15,"menu_order":5,"template":"","meta":{"_candela_citation":"[{\"type\":\"original\",\"description\":\"Revision and Adaptation\",\"author\":\"\",\"organization\":\"Lumen Learning\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Math in Society\",\"author\":\"Open Textbook Store, Transition Math Project, and the Open Course Library\",\"organization\":\"\",\"url\":\"http:\/\/www.opentextbookstore.com\/mathinsociety\/\",\"project\":\"\",\"license\":\"cc-by-sa\",\"license_terms\":\"\"}]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":76,"module-header":"learn_it","content_attributions":[{"type":"original","description":"Revision and Adaptation","author":"","organization":"Lumen Learning","url":"","project":"","license":"cc-by","license_terms":""},{"type":"cc","description":"Math in Society","author":"Open Textbook Store, Transition Math Project, and the Open Course Library","organization":"","url":"http:\/\/www.opentextbookstore.com\/mathinsociety\/","project":"","license":"cc-by-sa","license_terms":""}],"internal_book_links":[],"video_content":null,"cc_video_embed_content":{"cc_scripts":"","media_targets":[]},"try_it_collection":null,"_links":{"self":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters\/79"}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/users\/15"}],"version-history":[{"count":19,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters\/79\/revisions"}],"predecessor-version":[{"id":13583,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters\/79\/revisions\/13583"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/parts\/76"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters\/79\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/media?parent=79"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapter-type?post=79"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/contributor?post=79"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/license?post=79"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}