{"id":988,"date":"2024-04-27T14:22:56","date_gmt":"2024-04-27T18:22:56","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/?post_type=chapter&#038;p=988"},"modified":"2024-06-11T16:00:44","modified_gmt":"2024-06-11T20:00:44","slug":"basic-probability-rules-and-or-given","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/chapter\/basic-probability-rules-and-or-given\/","title":{"raw":"Basic Probability Rules (AND, OR, GIVEN)","rendered":"Basic Probability Rules (AND, OR, GIVEN)"},"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\nUnderstand the 'AND', 'OR' and 'Given' probability rules\r\n\r\n<\/div>\r\n<\/div>\r\n[embed]https:\/\/youtu.be\/4zF_kY29kTM[\/embed]\r\n<h1>AND (\u2229)<\/h1>\r\n<ul>\r\n \t<li>Also known as the intersection<\/li>\r\n \t<li>The 'overlap' between two groups or events.<\/li>\r\n \t<li>[latex] P(A \\text{ and } B) = P(A|B) \\times P(B) = P(B|A) \\times P(A)[\/latex]<\/li>\r\n \t<li><span style=\"text-align: initial\">It does not matter which event, A or B, 'occurred' first: [latex] P(A \\text{ and } B)= P(B \\text{ and } A)[\/latex]<\/span><\/li>\r\n<\/ul>\r\n<h1>OR (\u222a)<\/h1>\r\n<ul>\r\n \t<li>Also known as the union<\/li>\r\n \t<li>Includes all of both groups or events<\/li>\r\n \t<li>[latex] P(A \\text{ or } B) = P(A) + P(B) - P(A \\text{ and } B)[\/latex]<\/li>\r\n \t<li><span style=\"text-align: initial\">It does not matter which event, A or B, 'occurred' first<\/span>: [latex] P(A \\text{ or } B)= P(B \\text{ or } A)[\/latex]<\/li>\r\n<\/ul>\r\n<h1>Given (|)<\/h1>\r\n<ul>\r\n \t<li>Also known as a conditional probability<\/li>\r\n \t<li>Is the odds of one event occurring given that another event has already occurred<\/li>\r\n \t<li>The odds of 'A' occurring given that 'B' has already occurred: [latex] P(A | B) = \\frac{P(A \\text{ and } B)}{P(B)}[\/latex]<\/li>\r\n \t<li>The odds of 'B' occurring given that 'A' has already occurred: [latex] P(B | A) = \\frac{P(A \\text{ and } B)}{P(A)}[\/latex]<\/li>\r\n \t<li>The order of the events, A or B, matters: [latex] P(B | A) \\neq P(A | B)[\/latex]<\/li>\r\n<\/ul>\r\n<h1>A First BasiC Example<\/h1>\r\n<h2>Example 15.1<\/h2>\r\n<span style=\"color: #003366\"><strong>Problem Setup<\/strong><\/span>: Let P(A) = 0.80, P(B) = 0.70, P(A|B) = 0.25\r\n\r\n<strong><span style=\"color: #003366\">Questions<\/span><\/strong>: Can you solve for the following probabilities? And can you find the issue?\r\n<ol>\r\n \t<li>P(A and B)<\/li>\r\n \t<li>P(A or B)<\/li>\r\n \t<li>P(not A)<\/li>\r\n \t<li>P(not B)<\/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>. Click below to reveal the answers one at a time. Also see the next section for video solutions.\r\n\r\n[h5p id=\"33\"]\r\n<h1>A second basic example<\/h1>\r\n<h2>Example 15.2<\/h2>\r\n<span style=\"color: #003366\"><strong>Problem Setup<\/strong><\/span>: Let P(A) = 0.50, P(B) = 0.60, P(A and B) = 0.25\r\n\r\n<strong><span style=\"color: #003366\">Questions<\/span><\/strong>: Can you solve for the following probabilities?\r\n<ol>\r\n \t<li>P(A | B)<\/li>\r\n \t<li>P(B | A)<\/li>\r\n \t<li>P(A or B)<\/li>\r\n \t<li>P(not B)<\/li>\r\n<\/ol>\r\n<strong><span style=\"color: #003366\">Solution<\/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>. Click below to reveal the answers one at a time.\u00a0 Also see the next section for video solutions.\r\n\r\n[h5p id=\"34\"]\r\n<h1>Video Walkthrough of TWO BasiC ExampleS<\/h1>\r\n[embed]https:\/\/youtu.be\/9Jd51Xtz7rM[\/embed]\r\n<h1>Key Takeaways (EXERCISE)<\/h1>\r\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Key Takeaways: Basic Probability Rules (AND, OR, GIVEN)<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\n[h5p id=\"31\"]\r\n\r\n[h5p id=\"32\"]\r\n\r\n<\/div>\r\n<\/div>\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>Understand the &#8216;AND&#8217;, &#8216;OR&#8217; and &#8216;Given&#8217; probability rules<\/p>\n<\/div>\n<\/div>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"The probability rules (and, or given)\" width=\"500\" height=\"375\" src=\"https:\/\/www.youtube.com\/embed\/4zF_kY29kTM?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<h1>AND (\u2229)<\/h1>\n<ul>\n<li>Also known as the intersection<\/li>\n<li>The &#8216;overlap&#8217; between two groups or events.<\/li>\n<li>[latex]P(A \\text{ and } B) = P(A|B) \\times P(B) = P(B|A) \\times P(A)[\/latex]<\/li>\n<li><span style=\"text-align: initial\">It does not matter which event, A or B, &#8216;occurred&#8217; first: [latex]P(A \\text{ and } B)= P(B \\text{ and } A)[\/latex]<\/span><\/li>\n<\/ul>\n<h1>OR (\u222a)<\/h1>\n<ul>\n<li>Also known as the union<\/li>\n<li>Includes all of both groups or events<\/li>\n<li>[latex]P(A \\text{ or } B) = P(A) + P(B) - P(A \\text{ and } B)[\/latex]<\/li>\n<li><span style=\"text-align: initial\">It does not matter which event, A or B, &#8216;occurred&#8217; first<\/span>: [latex]P(A \\text{ or } B)= P(B \\text{ or } A)[\/latex]<\/li>\n<\/ul>\n<h1>Given (|)<\/h1>\n<ul>\n<li>Also known as a conditional probability<\/li>\n<li>Is the odds of one event occurring given that another event has already occurred<\/li>\n<li>The odds of &#8216;A&#8217; occurring given that &#8216;B&#8217; has already occurred: [latex]P(A | B) = \\frac{P(A \\text{ and } B)}{P(B)}[\/latex]<\/li>\n<li>The odds of &#8216;B&#8217; occurring given that &#8216;A&#8217; has already occurred: [latex]P(B | A) = \\frac{P(A \\text{ and } B)}{P(A)}[\/latex]<\/li>\n<li>The order of the events, A or B, matters: [latex]P(B | A) \\neq P(A | B)[\/latex]<\/li>\n<\/ul>\n<h1>A First BasiC Example<\/h1>\n<h2>Example 15.1<\/h2>\n<p><span style=\"color: #003366\"><strong>Problem Setup<\/strong><\/span>: Let P(A) = 0.80, P(B) = 0.70, P(A|B) = 0.25<\/p>\n<p><strong><span style=\"color: #003366\">Questions<\/span><\/strong>: Can you solve for the following probabilities? And can you find the issue?<\/p>\n<ol>\n<li>P(A and B)<\/li>\n<li>P(A or B)<\/li>\n<li>P(not A)<\/li>\n<li>P(not B)<\/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>. Click below to reveal the answers one at a time. Also see the next section for video solutions.<\/p>\n<div id=\"h5p-33\">\n<div class=\"h5p-iframe-wrapper\"><iframe id=\"h5p-iframe-33\" class=\"h5p-iframe\" data-content-id=\"33\" style=\"height:1px\" src=\"about:blank\" frameBorder=\"0\" scrolling=\"no\" title=\"Example 15.1 - Probabilities Rules Example 1 Solutions\"><\/iframe><\/div>\n<\/div>\n<h1>A second basic example<\/h1>\n<h2>Example 15.2<\/h2>\n<p><span style=\"color: #003366\"><strong>Problem Setup<\/strong><\/span>: Let P(A) = 0.50, P(B) = 0.60, P(A and B) = 0.25<\/p>\n<p><strong><span style=\"color: #003366\">Questions<\/span><\/strong>: Can you solve for the following probabilities?<\/p>\n<ol>\n<li>P(A | B)<\/li>\n<li>P(B | A)<\/li>\n<li>P(A or B)<\/li>\n<li>P(not B)<\/li>\n<\/ol>\n<p><strong><span style=\"color: #003366\">Solution<\/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>. Click below to reveal the answers one at a time.\u00a0 Also see the next section for video solutions.<\/p>\n<div id=\"h5p-34\">\n<div class=\"h5p-iframe-wrapper\"><iframe id=\"h5p-iframe-34\" class=\"h5p-iframe\" data-content-id=\"34\" style=\"height:1px\" src=\"about:blank\" frameBorder=\"0\" scrolling=\"no\" title=\"Example 15.2 - Probabilities Rules Example 2 Solutions\"><\/iframe><\/div>\n<\/div>\n<h1>Video Walkthrough of TWO BasiC ExampleS<\/h1>\n<p><iframe loading=\"lazy\" id=\"oembed-2\" 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>Key Takeaways (EXERCISE)<\/h1>\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Key Takeaways: Basic Probability Rules (AND, OR, GIVEN)<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"h5p-31\">\n<div class=\"h5p-iframe-wrapper\"><iframe id=\"h5p-iframe-31\" class=\"h5p-iframe\" data-content-id=\"31\" style=\"height:1px\" src=\"about:blank\" frameBorder=\"0\" scrolling=\"no\" title=\"Key Takeaways for AND, OR, GIVEN\"><\/iframe><\/div>\n<\/div>\n<div id=\"h5p-32\">\n<div class=\"h5p-iframe-wrapper\"><iframe id=\"h5p-iframe-32\" class=\"h5p-iframe\" data-content-id=\"32\" style=\"height:1px\" src=\"about:blank\" frameBorder=\"0\" scrolling=\"no\" title=\"Key Takeaways for AND, OR, GIVEN\"><\/iframe><\/div>\n<\/div>\n<\/div>\n<\/div>\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":2,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-988","chapter","type-chapter","status-publish","hentry"],"part":208,"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/pressbooks\/v2\/chapters\/988","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":25,"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/pressbooks\/v2\/chapters\/988\/revisions"}],"predecessor-version":[{"id":1947,"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/pressbooks\/v2\/chapters\/988\/revisions\/1947"}],"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\/988\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/wp\/v2\/media?parent=988"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/pressbooks\/v2\/chapter-type?post=988"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/wp\/v2\/contributor?post=988"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/wp-json\/wp\/v2\/license?post=988"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}