{"id":984,"date":"2023-06-22T01:38:48","date_gmt":"2023-06-22T01:38:48","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/probability-apply-it-2\/"},"modified":"2025-05-10T22:30:27","modified_gmt":"2025-05-10T22:30:27","slug":"probability-apply-it-2","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/probability-apply-it-2\/","title":{"raw":"Probability: Apply It 2","rendered":"Probability: Apply It 2"},"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>Law of Large Numbers<\/h2>\r\n<p>Let's do an experiment for the duck pond game using the random number generator.<\/p>\r\n<p>[reveal-answer q=\"487048\"]Steps to generate random numbers[\/reveal-answer]<br \/>\r\n[hidden-answer a=\"487048\"]<\/p>\r\n<p style=\"padding-left: 40px;\"><strong>Step 1: Choose Minimum<\/strong>: 1<\/p>\r\n<p style=\"padding-left: 40px;\"><strong>Step 2: Choose Maximum<\/strong>: 20<\/p>\r\n<p style=\"padding-left: 40px;\"><strong>Step 3: How many numbers would you like to generate<\/strong>? 1<\/p>\r\n<p style=\"padding-left: 40px;\"><strong>Step 4: Sample with Replacement<\/strong>? Yes. (We replace numbers here because we want to always pick from 20 possibilities.)<\/p>\r\n<p style=\"padding-left: 40px;\"><strong>Step 5: <\/strong>Select \u201c<strong>Frequency Table<\/strong>\u201d<\/p>\r\n<p style=\"padding-left: 40px;\"><strong>Step 6: <\/strong>Select \u201c<strong>Generate<\/strong>\u201d[\/hidden-answer]<\/p>\r\n<p><iframe src=\"https:\/\/lumen-learning.shinyapps.io\/randomnumbers\/\" width=\"100%\" height=\"850\"><\/iframe><\/p>\r\n<p>&nbsp;<\/p>\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]1397[\/ohm2_question]<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]1398[\/ohm2_question]<\/section>\r\n<p>What we are seeing here is referred to as the<strong> Law of Large Numbers.<\/strong><\/p>\r\n<section class=\"textbox keyTakeaway\">\r\n<h3>law of large numbers<\/h3>\r\n<p>The <strong>Law of Large Numbers<\/strong> says that as we increase the number of times we repeat a chance experiment, the closer we can expect the empirical probability calculated from our chance experiment to be to the true probability.<\/p>\r\n<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]850[\/ohm2_question]<\/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>Law of Large Numbers<\/h2>\n<p>Let&#8217;s do an experiment for the duck pond game using the random number generator.<\/p>\n<p><div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q487048\">Steps to generate random numbers<\/button><\/p>\n<div id=\"q487048\" class=\"hidden-answer\" style=\"display: none\">\n<p style=\"padding-left: 40px;\"><strong>Step 1: Choose Minimum<\/strong>: 1<\/p>\n<p style=\"padding-left: 40px;\"><strong>Step 2: Choose Maximum<\/strong>: 20<\/p>\n<p style=\"padding-left: 40px;\"><strong>Step 3: How many numbers would you like to generate<\/strong>? 1<\/p>\n<p style=\"padding-left: 40px;\"><strong>Step 4: Sample with Replacement<\/strong>? Yes. (We replace numbers here because we want to always pick from 20 possibilities.)<\/p>\n<p style=\"padding-left: 40px;\"><strong>Step 5: <\/strong>Select \u201c<strong>Frequency Table<\/strong>\u201d<\/p>\n<p style=\"padding-left: 40px;\"><strong>Step 6: <\/strong>Select \u201c<strong>Generate<\/strong>\u201d<\/div>\n<\/div>\n<p><iframe loading=\"lazy\" src=\"https:\/\/lumen-learning.shinyapps.io\/randomnumbers\/\" width=\"100%\" height=\"850\"><\/iframe><\/p>\n<p>&nbsp;<\/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=\"ohm1397\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=1397&theme=lumen&iframe_resize_id=ohm1397&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm1398\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=1398&theme=lumen&iframe_resize_id=ohm1398&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<p>What we are seeing here is referred to as the<strong> Law of Large Numbers.<\/strong><\/p>\n<section class=\"textbox keyTakeaway\">\n<h3>law of large numbers<\/h3>\n<p>The <strong>Law of Large Numbers<\/strong> says that as we increase the number of times we repeat a chance experiment, the closer we can expect the empirical probability calculated from our chance experiment to be to the true probability.<\/p>\n<\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm850\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=850&theme=lumen&iframe_resize_id=ohm850&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n","protected":false},"author":8,"menu_order":8,"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":"apply_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\/984"}],"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\/8"}],"version-history":[{"count":7,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/984\/revisions"}],"predecessor-version":[{"id":6534,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/984\/revisions\/6534"}],"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\/984\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=984"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=984"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=984"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=984"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}