{"id":986,"date":"2023-06-22T01:38:49","date_gmt":"2023-06-22T01:38:49","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/probabilities-of-two-events-background-youll-need-1\/"},"modified":"2025-05-10T22:20:04","modified_gmt":"2025-05-10T22:20:04","slug":"probabilities-of-two-events-background-youll-need-1","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/probabilities-of-two-events-background-youll-need-1\/","title":{"raw":"Probability: Background You'll Need 2","rendered":"Probability: Background You&#8217;ll Need 2"},"content":{"raw":"<section class=\"textbox learningGoals\">\r\n<ul>\r\n\t<li>Build contingency (two-way) tables.<\/li>\r\n<\/ul>\r\n<\/section>\r\n<h2>Contingency Tables<\/h2>\r\n<p>We use a <strong>contingency table<\/strong>, sometimes called a <strong>two-way table<\/strong>, to organize data on two categorical variables at the same time.<\/p>\r\n<section class=\"textbox keyTakeaway\">\r\n<h3>two-way table<\/h3>\r\n<p>A <strong>two-way table<\/strong>, also known as a <strong>contingency table<\/strong>, is a table used in statistics to represent the relationship between two categorical variables.<\/p>\r\n<p>&nbsp;<\/p>\r\n<p>A contingency table provides a way of portraying data for two categorical variables that can help calculate probabilities. The table displays sample values in relation to two different variables that may be dependent or contingent on one another.<\/p>\r\n<\/section>\r\n<section class=\"textbox example\">\r\n<h3>Example<\/h3>\r\n<p>This table shows the number of athletes who stretch before exercising and how many had injuries within the past year.<\/p>\r\n<table>\r\n<thead>\r\n<tr>\r\n<th>\u00a0<\/th>\r\n<th>Injury in last year<\/th>\r\n<th>No injury in last year<\/th>\r\n<th>Total<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr>\r\n<td><strong>Stretch<\/strong><\/td>\r\n<td>[latex]55[\/latex]<\/td>\r\n<td>[latex]295[\/latex]<\/td>\r\n<td>[latex]350[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><strong>Does not stretch<\/strong><\/td>\r\n<td>[latex]231[\/latex]<\/td>\r\n<td>[latex]219[\/latex]<\/td>\r\n<td>[latex]450[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><strong>Total<\/strong><\/td>\r\n<td>[latex]286[\/latex]<\/td>\r\n<td>[latex]514[\/latex]<\/td>\r\n<td><strong>[latex]800[\/latex]<\/strong><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<ol>\r\n\t<li>What proportion of athletes stretch before exercising?<\/li>\r\n\t<li>What proportion of athletes had no injury in the last year?<\/li>\r\n\t<li>Describe the cell with [latex]55[\/latex] counts using a complete sentence.<\/li>\r\n<\/ol>\r\n<p>[reveal-answer q=\"124076\"]Show solution[\/reveal-answer]<br \/>\r\n[hidden-answer a=\"124076\"]<\/p>\r\n<ol>\r\n\t<li>Proportion of athletes who stretch before exercising = [latex]\\displaystyle\\frac{{350}}{{800}} = 0.4375[\/latex]<\/li>\r\n\t<li>Proportion of athletes that had no injury in the last year = [latex]\\displaystyle\\frac{{514}}{{800}} = 0.6425[\/latex]<\/li>\r\n\t<li>[latex]55[\/latex] athletes got injured AND stretched before exercising in the last year.<\/li>\r\n<\/ol>\r\n<p>[\/hidden-answer]<\/p>\r\n<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]1412[\/ohm2_question]<\/section>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li>Build contingency (two-way) tables.<\/li>\n<\/ul>\n<\/section>\n<h2>Contingency Tables<\/h2>\n<p>We use a <strong>contingency table<\/strong>, sometimes called a <strong>two-way table<\/strong>, to organize data on two categorical variables at the same time.<\/p>\n<section class=\"textbox keyTakeaway\">\n<h3>two-way table<\/h3>\n<p>A <strong>two-way table<\/strong>, also known as a <strong>contingency table<\/strong>, is a table used in statistics to represent the relationship between two categorical variables.<\/p>\n<p>&nbsp;<\/p>\n<p>A contingency table provides a way of portraying data for two categorical variables that can help calculate probabilities. The table displays sample values in relation to two different variables that may be dependent or contingent on one another.<\/p>\n<\/section>\n<section class=\"textbox example\">\n<h3>Example<\/h3>\n<p>This table shows the number of athletes who stretch before exercising and how many had injuries within the past year.<\/p>\n<table>\n<thead>\n<tr>\n<th>\u00a0<\/th>\n<th>Injury in last year<\/th>\n<th>No injury in last year<\/th>\n<th>Total<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td><strong>Stretch<\/strong><\/td>\n<td>[latex]55[\/latex]<\/td>\n<td>[latex]295[\/latex]<\/td>\n<td>[latex]350[\/latex]<\/td>\n<\/tr>\n<tr>\n<td><strong>Does not stretch<\/strong><\/td>\n<td>[latex]231[\/latex]<\/td>\n<td>[latex]219[\/latex]<\/td>\n<td>[latex]450[\/latex]<\/td>\n<\/tr>\n<tr>\n<td><strong>Total<\/strong><\/td>\n<td>[latex]286[\/latex]<\/td>\n<td>[latex]514[\/latex]<\/td>\n<td><strong>[latex]800[\/latex]<\/strong><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<ol>\n<li>What proportion of athletes stretch before exercising?<\/li>\n<li>What proportion of athletes had no injury in the last year?<\/li>\n<li>Describe the cell with [latex]55[\/latex] counts using a complete sentence.<\/li>\n<\/ol>\n<p><div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q124076\">Show solution<\/button><\/p>\n<div id=\"q124076\" class=\"hidden-answer\" style=\"display: none\">\n<ol>\n<li>Proportion of athletes who stretch before exercising = [latex]\\displaystyle\\frac{{350}}{{800}} = 0.4375[\/latex]<\/li>\n<li>Proportion of athletes that had no injury in the last year = [latex]\\displaystyle\\frac{{514}}{{800}} = 0.6425[\/latex]<\/li>\n<li>[latex]55[\/latex] athletes got injured AND stretched before exercising in the last year.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm1412\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=1412&theme=lumen&iframe_resize_id=ohm1412&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n","protected":false},"author":8,"menu_order":3,"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":"background_you_need","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\/986"}],"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":9,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/986\/revisions"}],"predecessor-version":[{"id":6525,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/986\/revisions\/6525"}],"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\/986\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=986"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=986"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=986"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=986"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}