{"id":1023,"date":"2024-04-27T16:09:45","date_gmt":"2024-04-27T20:09:45","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/?post_type=chapter&#038;p=1023"},"modified":"2024-05-11T11:19:23","modified_gmt":"2024-05-11T15:19:23","slug":"an-applied-example-of-conditional-probabilities","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/chapter\/an-applied-example-of-conditional-probabilities\/","title":{"raw":"An Applied Example Walk-Through","rendered":"An Applied Example Walk-Through"},"content":{"raw":"<div class=\"textbox textbox--learning-objectives\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\"><code><\/code>\u00a0Learning Objectives<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nApply the probability rules to a real world problem\r\n\r\n<\/div>\r\n<\/div>\r\nConditional probabilities are used in so many contexts and so many places in the real world:\r\n<ul>\r\n \t<li>What <a href=\"https:\/\/support.google.com\/google-ads\/answer\/2615875?hl=en#:~:text=CTR%20is%20the%20number%20of,your%20CTR%20would%20be%205%25.\">percent of people who view your ad click through<\/a>?<\/li>\r\n \t<li>What <a href=\"https:\/\/www.cmhc-schl.gc.ca\/blog\/2023\/rising-rates-homeowners-greatest-shocks-lie-ahead\">percent of people will default on their mortgages if they rase interest rates<\/a>?<\/li>\r\n \t<li>What <a href=\"https:\/\/www.merckmanuals.com\/en-ca\/professional\/special-subjects\/clinical-decision-making\/understanding-medical-tests-and-test-results\">percent of medical tests accurately report whether a person has an illness or not<\/a>?<\/li>\r\n \t<li>What <a href=\"https:\/\/data.world\/nrippner\/cancer-linear-regression-model-tutorial\">percent of people who have low incomes in the US survive cancer<\/a>?<\/li>\r\n<\/ul>\r\n<h1>Setting up an Applied Example<\/h1>\r\n<h2>Example 16.1.1<\/h2>\r\n<span style=\"color: #003366\"><strong>Problem Setup<\/strong><\/span>: A patient takes a lab test and the result comes back positive.\r\n<ul>\r\n \t<li>The test returns a positive result in 97% of the cases in which the disease is actually present.<\/li>\r\n \t<li>The test returns a negative result in 98% of the cases in which the disease is not present.<\/li>\r\n \t<li>0.8% of all people have this illness.<\/li>\r\n<\/ul>\r\n<span style=\"color: #003366\"><strong>Question: <\/strong><\/span>\r\n<ul>\r\n \t<li><span style=\"color: #003366\"><span style=\"color: #333333\">Can you write out the above sentences as probability expressions? <\/span><\/span><\/li>\r\n \t<li><span style=\"color: #003366\"><span style=\"color: #333333\">Check your answers against the solutions below (click to reveal).<\/span><\/span><\/li>\r\n<\/ul>\r\n<strong><span style=\"color: #003366\">Solutions:<\/span><\/strong>\r\n\r\n[h5p id=\"35\"]\r\n<h2>Example 16.1.2<\/h2>\r\n<span style=\"color: #003366\"><strong>Questions:\u00a0<\/strong><\/span>\r\n<ol>\r\n \t<li>What is the probability that the person tests positive and has the disease?<\/li>\r\n \t<li>What is the probability that the person tests negative and has the disease?<\/li>\r\n \t<li>What is the probability that the person tests positive and does not have the disease?<\/li>\r\n<\/ol>\r\n<strong><span style=\"color: #003366\">Instructions: <\/span><\/strong>\r\n<ul>\r\n \t<li><span style=\"color: #333333\">Write out the probability expression for each above question. <\/span><\/li>\r\n \t<li><span style=\"color: #333333\"><span style=\"color: #003366\">Check your answers against the solutions below (click to reveal).<\/span><\/span><\/li>\r\n<\/ul>\r\n<strong><span style=\"color: #003366\">Solutions:<\/span><\/strong>\r\n\r\n[h5p id=\"36\"]\r\n<h1>SOlving an Applied Example<\/h1>\r\n<h2>Example 16.1.3<\/h2>\r\n<span style=\"color: #003366\"><strong>Instructions:\u00a0<\/strong><\/span>Use the information from the previous section to solve for the probabilities:\r\n<ol>\r\n \t<li>What is the probability that the person tests positive and has the disease?<\/li>\r\n \t<li>What is the probability that the person tests negative and has the disease?<\/li>\r\n \t<li>What is the probability that the person tests positive and does not have the disease?<\/li>\r\n<\/ol>\r\n<strong><span style=\"color: #003366\">Solutions<\/span><\/strong>: <a href=\"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-content\/uploads\/sites\/2128\/2024\/04\/ProbabilityReview_Solutions.pptx\">Click here to download the written solutions<\/a>. Also see the next section for video solutions.\r\n\r\n[h5p id=\"77\"]\r\n<h1>Video Walkthrough of Applied Example<\/h1>\r\n[embed]https:\/\/youtu.be\/9Jd51Xtz7rM[\/embed]\r\n<h1>Your Own Notes (EXERCISE)<\/h1>\r\n<ul>\r\n \t<li>Are there any notes you want to take from this section? Is there anything you'd like to copy and paste below?<\/li>\r\n \t<li>These notes are for you only (they will not be stored anywhere)<\/li>\r\n \t<li>Make sure to download them at the end to use as a reference<\/li>\r\n<\/ul>\r\n[h5p id=\"16\"]","rendered":"<div class=\"textbox textbox--learning-objectives\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\"><code><\/code>\u00a0Learning Objectives<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Apply the probability rules to a real world problem<\/p>\n<\/div>\n<\/div>\n<p>Conditional probabilities are used in so many contexts and so many places in the real world:<\/p>\n<ul>\n<li>What <a href=\"https:\/\/support.google.com\/google-ads\/answer\/2615875?hl=en#:~:text=CTR%20is%20the%20number%20of,your%20CTR%20would%20be%205%25.\">percent of people who view your ad click through<\/a>?<\/li>\n<li>What <a href=\"https:\/\/www.cmhc-schl.gc.ca\/blog\/2023\/rising-rates-homeowners-greatest-shocks-lie-ahead\">percent of people will default on their mortgages if they rase interest rates<\/a>?<\/li>\n<li>What <a href=\"https:\/\/www.merckmanuals.com\/en-ca\/professional\/special-subjects\/clinical-decision-making\/understanding-medical-tests-and-test-results\">percent of medical tests accurately report whether a person has an illness or not<\/a>?<\/li>\n<li>What <a href=\"https:\/\/data.world\/nrippner\/cancer-linear-regression-model-tutorial\">percent of people who have low incomes in the US survive cancer<\/a>?<\/li>\n<\/ul>\n<h1>Setting up an Applied Example<\/h1>\n<h2>Example 16.1.1<\/h2>\n<p><span style=\"color: #003366\"><strong>Problem Setup<\/strong><\/span>: A patient takes a lab test and the result comes back positive.<\/p>\n<ul>\n<li>The test returns a positive result in 97% of the cases in which the disease is actually present.<\/li>\n<li>The test returns a negative result in 98% of the cases in which the disease is not present.<\/li>\n<li>0.8% of all people have this illness.<\/li>\n<\/ul>\n<p><span style=\"color: #003366\"><strong>Question: <\/strong><\/span><\/p>\n<ul>\n<li><span style=\"color: #003366\"><span style=\"color: #333333\">Can you write out the above sentences as probability expressions? <\/span><\/span><\/li>\n<li><span style=\"color: #003366\"><span style=\"color: #333333\">Check your answers against the solutions below (click to reveal).<\/span><\/span><\/li>\n<\/ul>\n<p><strong><span style=\"color: #003366\">Solutions:<\/span><\/strong><\/p>\n<div id=\"h5p-35\">\n<div class=\"h5p-iframe-wrapper\"><iframe id=\"h5p-iframe-35\" class=\"h5p-iframe\" data-content-id=\"35\" style=\"height:1px\" src=\"about:blank\" frameBorder=\"0\" scrolling=\"no\" title=\"Example 16.1.1 - Writing out Probability Expressions Solutions\"><\/iframe><\/div>\n<\/div>\n<h2>Example 16.1.2<\/h2>\n<p><span style=\"color: #003366\"><strong>Questions:\u00a0<\/strong><\/span><\/p>\n<ol>\n<li>What is the probability that the person tests positive and has the disease?<\/li>\n<li>What is the probability that the person tests negative and has the disease?<\/li>\n<li>What is the probability that the person tests positive and does not have the disease?<\/li>\n<\/ol>\n<p><strong><span style=\"color: #003366\">Instructions: <\/span><\/strong><\/p>\n<ul>\n<li><span style=\"color: #333333\">Write out the probability expression for each above question. <\/span><\/li>\n<li><span style=\"color: #333333\"><span style=\"color: #003366\">Check your answers against the solutions below (click to reveal).<\/span><\/span><\/li>\n<\/ul>\n<p><strong><span style=\"color: #003366\">Solutions:<\/span><\/strong><\/p>\n<div id=\"h5p-36\">\n<div class=\"h5p-iframe-wrapper\"><iframe id=\"h5p-iframe-36\" class=\"h5p-iframe\" data-content-id=\"36\" style=\"height:1px\" src=\"about:blank\" frameBorder=\"0\" scrolling=\"no\" title=\"Example 16.1.2 Written Out Probability Expression Solutions\"><\/iframe><\/div>\n<\/div>\n<h1>SOlving an Applied Example<\/h1>\n<h2>Example 16.1.3<\/h2>\n<p><span style=\"color: #003366\"><strong>Instructions:\u00a0<\/strong><\/span>Use the information from the previous section to solve for the probabilities:<\/p>\n<ol>\n<li>What is the probability that the person tests positive and has the disease?<\/li>\n<li>What is the probability that the person tests negative and has the disease?<\/li>\n<li>What is the probability that the person tests positive and does not have the disease?<\/li>\n<\/ol>\n<p><strong><span style=\"color: #003366\">Solutions<\/span><\/strong>: <a href=\"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-content\/uploads\/sites\/2128\/2024\/04\/ProbabilityReview_Solutions.pptx\">Click here to download the written solutions<\/a>. Also see the next section for video solutions.<\/p>\n<div id=\"h5p-77\">\n<div class=\"h5p-iframe-wrapper\"><iframe id=\"h5p-iframe-77\" class=\"h5p-iframe\" data-content-id=\"77\" style=\"height:1px\" src=\"about:blank\" frameBorder=\"0\" scrolling=\"no\" title=\"Example 16.1.3 - Applied Probability Solutions\"><\/iframe><\/div>\n<\/div>\n<h1>Video Walkthrough of Applied Example<\/h1>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Basic examples with Probability rules\" width=\"500\" height=\"375\" src=\"https:\/\/www.youtube.com\/embed\/9Jd51Xtz7rM?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<h1>Your Own Notes (EXERCISE)<\/h1>\n<ul>\n<li>Are there any notes you want to take from this section? Is there anything you&#8217;d like to copy and paste below?<\/li>\n<li>These notes are for you only (they will not be stored anywhere)<\/li>\n<li>Make sure to download them at the end to use as a reference<\/li>\n<\/ul>\n<div id=\"h5p-16\">\n<div class=\"h5p-iframe-wrapper\"><iframe id=\"h5p-iframe-16\" class=\"h5p-iframe\" data-content-id=\"16\" style=\"height:1px\" src=\"about:blank\" frameBorder=\"0\" scrolling=\"no\" title=\"Key takeaways, notes and comments from this section document tool.\"><\/iframe><\/div>\n<\/div>\n","protected":false},"author":865,"menu_order":3,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-1023","chapter","type-chapter","status-publish","hentry"],"part":208,"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/pressbooks\/v2\/chapters\/1023","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/wp\/v2\/users\/865"}],"version-history":[{"count":12,"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/pressbooks\/v2\/chapters\/1023\/revisions"}],"predecessor-version":[{"id":1525,"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/pressbooks\/v2\/chapters\/1023\/revisions\/1525"}],"part":[{"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/pressbooks\/v2\/parts\/208"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/pressbooks\/v2\/chapters\/1023\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/wp\/v2\/media?parent=1023"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/pressbooks\/v2\/chapter-type?post=1023"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/wp\/v2\/contributor?post=1023"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/wp\/v2\/license?post=1023"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}