{"id":3013,"date":"2023-08-29T21:25:29","date_gmt":"2023-08-29T21:25:29","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/?post_type=chapter&#038;p=3013"},"modified":"2024-01-09T21:33:16","modified_gmt":"2024-01-09T21:33:16","slug":"probability-learn-it-1-2","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/probability-learn-it-1-2\/","title":{"raw":"Probability: Learn It 1","rendered":"Probability: Learn It 1"},"content":{"raw":"<section class=\"textbox learningGoals\">\r\n<ul>\r\n\t<li>Calculate the probability of an event in a chance experiment.<\/li>\r\n\t<li>Recognize the differences between theoretical and empirical probability.<\/li>\r\n<\/ul>\r\n<\/section>\r\n<h2>What is Probability?<\/h2>\r\n<section class=\"textbox keyTakeaway\">\r\n<h3>probability<\/h3>\r\n<p><strong>Probability<\/strong> is a measure that is associated with how certain we are of outcomes of a particular experiment or activity.<\/p>\r\n<\/section>\r\n<p>An <strong>experiment<\/strong>\u00a0is a planned operation carried out under controlled conditions. If the result is not predetermined, then the experiment is said to be a\u00a0chance experiment. A\u00a0<strong>chance experiment<\/strong>\u00a0involves making observations in situations where there is uncertainty about which of two or more possible\u00a0<strong>outcomes<\/strong>\u00a0will result. Flipping one fair coin is an example of a chance experiment.<\/p>\r\n<section class=\"textbox proTip\">An <strong>outcome<\/strong> of a chance experiment is a result that can happen when you do a chance experiment.<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]831[\/ohm2_question]<\/section>\r\n<section class=\"textbox keyTakeaway\">\r\n<h3>sample space<\/h3>\r\n<p>The <strong>sample space <\/strong>of a chance experiment is the collection of all possible outcomes for the experiment.<\/p>\r\n<p>The uppercase letter [latex]S[\/latex] is typically used to denote the sample space.<\/p>\r\n<\/section>\r\n<p>Let's see if we can simulate chance experiments to understand probability.<\/p>\r\n<section class=\"textbox interact\">Steps to simulate coin flips:\r\n\r\n\r\n<p style=\"padding-left: 40px;\"><strong>Step 1: <\/strong>Select the <strong>Coin Flips<\/strong>\u00a0tab.<\/p>\r\n<p style=\"padding-left: 40px;\"><strong>Step 2: <\/strong>On <strong>How many flips do you want to generate in one simulation?<\/strong>, enter [latex]1[\/latex], [latex]10[\/latex], [latex]100[\/latex], [latex]1000[\/latex], and [latex]10,000[\/latex], one after another.<\/p>\r\n<p style=\"padding-left: 40px;\"><strong>Step 3:<\/strong> Select <strong>Generate.<\/strong><\/p>\r\n<\/section>\r\n<iframe src=\"https:\/\/lumen-learning.shinyapps.io\/randomnumbers\/\" width=\"100%\" height=\"850\"><\/iframe>\r\n<p><br \/>\r\n[<a href=\"https:\/\/lumen-learning.shinyapps.io\/randomnumbers\/\" target=\"_blank\" rel=\"noopener\">Trouble viewing? Click to open in a new tab.<\/a>]<\/p>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]11789[\/ohm2_question]<\/section>\r\n<p>The proportions you found above from flipping a fair coin in [latex]1[\/latex], [latex]10[\/latex], [latex]100[\/latex], [latex]1,000[\/latex], and [latex]10,000[\/latex] simulations were empirical probabilities.<\/p>\r\n<section class=\"textbox keyTakeaway\">\r\n<h3>empirical probabilities<\/h3>\r\n<p>The probability estimated from a chance experiment is called an <strong>empirical probability<\/strong>.<\/p>\r\n<\/section>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li>Calculate the probability of an event in a chance experiment.<\/li>\n<li>Recognize the differences between theoretical and empirical probability.<\/li>\n<\/ul>\n<\/section>\n<h2>What is Probability?<\/h2>\n<section class=\"textbox keyTakeaway\">\n<h3>probability<\/h3>\n<p><strong>Probability<\/strong> is a measure that is associated with how certain we are of outcomes of a particular experiment or activity.<\/p>\n<\/section>\n<p>An <strong>experiment<\/strong>\u00a0is a planned operation carried out under controlled conditions. If the result is not predetermined, then the experiment is said to be a\u00a0chance experiment. A\u00a0<strong>chance experiment<\/strong>\u00a0involves making observations in situations where there is uncertainty about which of two or more possible\u00a0<strong>outcomes<\/strong>\u00a0will result. Flipping one fair coin is an example of a chance experiment.<\/p>\n<section class=\"textbox proTip\">An <strong>outcome<\/strong> of a chance experiment is a result that can happen when you do a chance experiment.<\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm831\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=831&theme=lumen&iframe_resize_id=ohm831&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox keyTakeaway\">\n<h3>sample space<\/h3>\n<p>The <strong>sample space <\/strong>of a chance experiment is the collection of all possible outcomes for the experiment.<\/p>\n<p>The uppercase letter [latex]S[\/latex] is typically used to denote the sample space.<\/p>\n<\/section>\n<p>Let&#8217;s see if we can simulate chance experiments to understand probability.<\/p>\n<section class=\"textbox interact\">Steps to simulate coin flips:<\/p>\n<p style=\"padding-left: 40px;\"><strong>Step 1: <\/strong>Select the <strong>Coin Flips<\/strong>\u00a0tab.<\/p>\n<p style=\"padding-left: 40px;\"><strong>Step 2: <\/strong>On <strong>How many flips do you want to generate in one simulation?<\/strong>, enter [latex]1[\/latex], [latex]10[\/latex], [latex]100[\/latex], [latex]1000[\/latex], and [latex]10,000[\/latex], one after another.<\/p>\n<p style=\"padding-left: 40px;\"><strong>Step 3:<\/strong> Select <strong>Generate.<\/strong><\/p>\n<\/section>\n<p><iframe loading=\"lazy\" src=\"https:\/\/lumen-learning.shinyapps.io\/randomnumbers\/\" width=\"100%\" height=\"850\"><\/iframe><\/p>\n<p>\n[<a href=\"https:\/\/lumen-learning.shinyapps.io\/randomnumbers\/\" target=\"_blank\" rel=\"noopener\">Trouble viewing? Click to open in a new tab.<\/a>]<\/p>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm11789\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=11789&theme=lumen&iframe_resize_id=ohm11789&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<p>The proportions you found above from flipping a fair coin in [latex]1[\/latex], [latex]10[\/latex], [latex]100[\/latex], [latex]1,000[\/latex], and [latex]10,000[\/latex] simulations were empirical probabilities.<\/p>\n<section class=\"textbox keyTakeaway\">\n<h3>empirical probabilities<\/h3>\n<p>The probability estimated from a chance experiment is called an <strong>empirical probability<\/strong>.<\/p>\n<\/section>\n","protected":false},"author":12,"menu_order":4,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":974,"module-header":"learn_it","content_attributions":[],"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\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/3013"}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/users\/12"}],"version-history":[{"count":17,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/3013\/revisions"}],"predecessor-version":[{"id":4974,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/3013\/revisions\/4974"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/parts\/974"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/3013\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=3013"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=3013"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=3013"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=3013"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}