{"id":253,"date":"2017-04-15T03:20:12","date_gmt":"2017-04-15T03:20:12","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/conceptstest1\/chapter\/two-way-tables-3-of-5\/"},"modified":"2017-05-29T01:08:20","modified_gmt":"2017-05-29T01:08:20","slug":"two-way-tables-3-of-5","status":"web-only","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/suny-hccc-wm-concepts-statistics\/chapter\/two-way-tables-3-of-5\/","title":{"raw":"Two-Way Tables (3 of 5)","rendered":"Two-Way Tables (3 of 5)"},"content":{"raw":"&nbsp;\r\n<div class=\"textbox learning-objectives\">\r\n<h3>Learning Objectives<\/h3>\r\n<ul>\r\n \t<li>Calculate marginal, joint, and conditional percentages and interpret them as probability estimates.<\/li>\r\n<\/ul>\r\n<\/div>\r\nAt this point, we know how to determine <em>marginal probabilities<\/em>, such as the probability that a randomly selected student is female: <em>P<\/em>(female).\r\n\r\nAnd we know how to calculate <em>conditional probabilities<\/em>, such as the probability that a randomly selected female student is in the Health Science program: <em>P<\/em>(Health Science | female)\r\n\r\nBut we do not know how to calculate <strong>joint probabilities<\/strong>, such as the probability that a randomly selected student is both a female <em>and<\/em> in the Health Sciences program.\r\n\r\nWe write this joint probability as <em>P<\/em>(female and Health Sciences).\r\n\r\nThe following example illustrates how to calculate a joint probability.\r\n<div class=\"textbox examples\">\r\n<h3>Example<\/h3>\r\n<h2>Joint Probability<\/h2>\r\n<strong>Question:<\/strong> <em>If we select a student at random, what is the probability that the student is both a male <strong>and <\/strong>in the Info Tech program?<\/em>\r\n\r\n<strong>Answer:<\/strong> This question involves male students who are in the Info Tech program, but it is NOT a conditional probability. We are picking a student at random from the <em>entire population of 12,000 students<\/em>, so there is no condition. Our shorthand notation for this probability is:\r\n<ul style=\"list-style-type: none\">\r\n \t<li><em>P<\/em>(male <strong>and <\/strong>Info Tech)<\/li>\r\n<\/ul>\r\nSince 564 of the 12,000 students enrolled at the college are both male and in the Info Tech program (see table), the probability <em>P<\/em>(male and Info Tech) is:\r\n<p style=\"text-align: center\">[latex]\\frac{\\text{564}}{\\text{12,000}}\\approx \\text{.05}[\/latex]<\/p>\r\n\r\n<table>\r\n<tbody>\r\n<tr class=\"oli_table\" style=\"height: 30.3906px\">\r\n<td style=\"height: 30.3906px\"><\/td>\r\n<td style=\"height: 30.3906px\"><strong>Arts-Sci<\/strong><\/td>\r\n<td style=\"height: 30.3906px\"><strong>Bus-Econ<\/strong><\/td>\r\n<td style=\"height: 30.3906px\" align=\"center\"><strong>Info Tech<\/strong><\/td>\r\n<td style=\"height: 30.3906px\" align=\"center\"><strong>Health Science<\/strong><\/td>\r\n<td style=\"height: 30.3906px\" align=\"center\"><strong>Graphics Design<\/strong><\/td>\r\n<td style=\"height: 30.3906px\" align=\"center\"><strong>Culinary Arts<\/strong><\/td>\r\n<td style=\"height: 30.3906px\" align=\"center\"><strong>Row Totals<\/strong><\/td>\r\n<\/tr>\r\n<tr class=\"oli_table\" style=\"height: 15px\">\r\n<td style=\"height: 15px\" align=\"center\"><strong>Female<\/strong><\/td>\r\n<td style=\"height: 15px\" align=\"center\">4,660<\/td>\r\n<td style=\"height: 15px\" align=\"center\">435<\/td>\r\n<td style=\"height: 15px\" align=\"center\">494<\/td>\r\n<td style=\"height: 15px\" align=\"center\">421<\/td>\r\n<td style=\"height: 15px\" align=\"center\">105<\/td>\r\n<td style=\"height: 15px\" align=\"center\">83<\/td>\r\n<td style=\"height: 15px\" align=\"center\">6,198<\/td>\r\n<\/tr>\r\n<tr class=\"oli_table\" style=\"height: 15px\">\r\n<td style=\"height: 15px\" align=\"center\"><strong>Male<\/strong><\/td>\r\n<td style=\"height: 15px\" align=\"center\">4,334<\/td>\r\n<td style=\"height: 15px\" align=\"center\">490<\/td>\r\n<td style=\"height: 15px\" align=\"center\"><strong><strong class=\"oli_term\">564<\/strong><\/strong><\/td>\r\n<td style=\"height: 15px\" align=\"center\">223<\/td>\r\n<td style=\"height: 15px\" align=\"center\">97<\/td>\r\n<td style=\"height: 15px\" align=\"center\">94<\/td>\r\n<td style=\"height: 15px\" align=\"center\">5,802<\/td>\r\n<\/tr>\r\n<tr class=\"oli_table\" style=\"height: 30px\">\r\n<td style=\"height: 30px\" align=\"center\"><strong>Column Totals<\/strong><\/td>\r\n<td style=\"height: 30px\" align=\"center\">8,994<\/td>\r\n<td style=\"height: 30px\" align=\"center\">925<\/td>\r\n<td style=\"height: 30px\" align=\"center\">1,058<\/td>\r\n<td style=\"height: 30px\" align=\"center\">644<\/td>\r\n<td style=\"height: 30px\" align=\"center\">202<\/td>\r\n<td style=\"height: 30px\" align=\"center\">177<\/td>\r\n<td style=\"height: 30px\" align=\"center\"><strong><strong class=\"oli_term\">12,000<\/strong><\/strong><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nWe call this calculation a <strong>joint probability<\/strong>. Note that when we calculate a joint probability, we divide the count from an inner cell of the table by the overall total count in the lower right corner.\r\n\r\n<\/div>\r\nThe following table is used for the next Learn By Doing and Did I Get This? activities.\r\n<table>\r\n<tbody>\r\n<tr class=\"oli_table\">\r\n<td><\/td>\r\n<td><strong>Arts-Sci<\/strong><\/td>\r\n<td><strong>Bus-Econ<\/strong><\/td>\r\n<td><strong>Info Tech<\/strong><\/td>\r\n<td><strong>Health Science<\/strong><\/td>\r\n<td><strong>Graphics Design<\/strong><\/td>\r\n<td><strong>Culinary Arts<\/strong><\/td>\r\n<td align=\"center\"><strong>Row Totals<\/strong><\/td>\r\n<\/tr>\r\n<tr class=\"oli_table\">\r\n<td align=\"center\"><strong>Female<\/strong><\/td>\r\n<td align=\"center\">4,660<\/td>\r\n<td align=\"center\">435<\/td>\r\n<td align=\"center\">494<\/td>\r\n<td align=\"center\">421<\/td>\r\n<td align=\"center\">105<\/td>\r\n<td align=\"center\">83<\/td>\r\n<td align=\"center\">6,198<\/td>\r\n<\/tr>\r\n<tr class=\"oli_table\">\r\n<td align=\"center\"><strong>Male<\/strong><\/td>\r\n<td align=\"center\">4,334<\/td>\r\n<td align=\"center\">490<\/td>\r\n<td align=\"center\">564<\/td>\r\n<td align=\"center\">223<\/td>\r\n<td align=\"center\">97<\/td>\r\n<td align=\"center\">94<\/td>\r\n<td align=\"center\">5,802<\/td>\r\n<\/tr>\r\n<tr class=\"oli_table\">\r\n<td align=\"center\"><strong>Column Totals<\/strong><\/td>\r\n<td align=\"center\">8,994<\/td>\r\n<td align=\"center\">925<\/td>\r\n<td align=\"center\">1,058<\/td>\r\n<td align=\"center\">644<\/td>\r\n<td align=\"center\">202<\/td>\r\n<td align=\"center\">177<\/td>\r\n<td align=\"center\">12,000<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<div class=\"textbox exercises\">\r\n<h3>Learn By Doing<\/h3>\r\nhttps:\/\/assessments.lumenlearning.com\/assessments\/3540\r\n\r\nhttps:\/\/assessments.lumenlearning.com\/assessments\/3541\r\n\r\n<\/div>\r\n&nbsp;","rendered":"<p>&nbsp;<\/p>\n<div class=\"textbox learning-objectives\">\n<h3>Learning Objectives<\/h3>\n<ul>\n<li>Calculate marginal, joint, and conditional percentages and interpret them as probability estimates.<\/li>\n<\/ul>\n<\/div>\n<p>At this point, we know how to determine <em>marginal probabilities<\/em>, such as the probability that a randomly selected student is female: <em>P<\/em>(female).<\/p>\n<p>And we know how to calculate <em>conditional probabilities<\/em>, such as the probability that a randomly selected female student is in the Health Science program: <em>P<\/em>(Health Science | female)<\/p>\n<p>But we do not know how to calculate <strong>joint probabilities<\/strong>, such as the probability that a randomly selected student is both a female <em>and<\/em> in the Health Sciences program.<\/p>\n<p>We write this joint probability as <em>P<\/em>(female and Health Sciences).<\/p>\n<p>The following example illustrates how to calculate a joint probability.<\/p>\n<div class=\"textbox examples\">\n<h3>Example<\/h3>\n<h2>Joint Probability<\/h2>\n<p><strong>Question:<\/strong> <em>If we select a student at random, what is the probability that the student is both a male <strong>and <\/strong>in the Info Tech program?<\/em><\/p>\n<p><strong>Answer:<\/strong> This question involves male students who are in the Info Tech program, but it is NOT a conditional probability. We are picking a student at random from the <em>entire population of 12,000 students<\/em>, so there is no condition. Our shorthand notation for this probability is:<\/p>\n<ul style=\"list-style-type: none\">\n<li><em>P<\/em>(male <strong>and <\/strong>Info Tech)<\/li>\n<\/ul>\n<p>Since 564 of the 12,000 students enrolled at the college are both male and in the Info Tech program (see table), the probability <em>P<\/em>(male and Info Tech) is:<\/p>\n<p style=\"text-align: center\">[latex]\\frac{\\text{564}}{\\text{12,000}}\\approx \\text{.05}[\/latex]<\/p>\n<table>\n<tbody>\n<tr class=\"oli_table\" style=\"height: 30.3906px\">\n<td style=\"height: 30.3906px\"><\/td>\n<td style=\"height: 30.3906px\"><strong>Arts-Sci<\/strong><\/td>\n<td style=\"height: 30.3906px\"><strong>Bus-Econ<\/strong><\/td>\n<td style=\"height: 30.3906px\" align=\"center\"><strong>Info Tech<\/strong><\/td>\n<td style=\"height: 30.3906px\" align=\"center\"><strong>Health Science<\/strong><\/td>\n<td style=\"height: 30.3906px\" align=\"center\"><strong>Graphics Design<\/strong><\/td>\n<td style=\"height: 30.3906px\" align=\"center\"><strong>Culinary Arts<\/strong><\/td>\n<td style=\"height: 30.3906px\" align=\"center\"><strong>Row Totals<\/strong><\/td>\n<\/tr>\n<tr class=\"oli_table\" style=\"height: 15px\">\n<td style=\"height: 15px\" align=\"center\"><strong>Female<\/strong><\/td>\n<td style=\"height: 15px\" align=\"center\">4,660<\/td>\n<td style=\"height: 15px\" align=\"center\">435<\/td>\n<td style=\"height: 15px\" align=\"center\">494<\/td>\n<td style=\"height: 15px\" align=\"center\">421<\/td>\n<td style=\"height: 15px\" align=\"center\">105<\/td>\n<td style=\"height: 15px\" align=\"center\">83<\/td>\n<td style=\"height: 15px\" align=\"center\">6,198<\/td>\n<\/tr>\n<tr class=\"oli_table\" style=\"height: 15px\">\n<td style=\"height: 15px\" align=\"center\"><strong>Male<\/strong><\/td>\n<td style=\"height: 15px\" align=\"center\">4,334<\/td>\n<td style=\"height: 15px\" align=\"center\">490<\/td>\n<td style=\"height: 15px\" align=\"center\"><strong><strong class=\"oli_term\">564<\/strong><\/strong><\/td>\n<td style=\"height: 15px\" align=\"center\">223<\/td>\n<td style=\"height: 15px\" align=\"center\">97<\/td>\n<td style=\"height: 15px\" align=\"center\">94<\/td>\n<td style=\"height: 15px\" align=\"center\">5,802<\/td>\n<\/tr>\n<tr class=\"oli_table\" style=\"height: 30px\">\n<td style=\"height: 30px\" align=\"center\"><strong>Column Totals<\/strong><\/td>\n<td style=\"height: 30px\" align=\"center\">8,994<\/td>\n<td style=\"height: 30px\" align=\"center\">925<\/td>\n<td style=\"height: 30px\" align=\"center\">1,058<\/td>\n<td style=\"height: 30px\" align=\"center\">644<\/td>\n<td style=\"height: 30px\" align=\"center\">202<\/td>\n<td style=\"height: 30px\" align=\"center\">177<\/td>\n<td style=\"height: 30px\" align=\"center\"><strong><strong class=\"oli_term\">12,000<\/strong><\/strong><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>We call this calculation a <strong>joint probability<\/strong>. Note that when we calculate a joint probability, we divide the count from an inner cell of the table by the overall total count in the lower right corner.<\/p>\n<\/div>\n<p>The following table is used for the next Learn By Doing and Did I Get This? activities.<\/p>\n<table>\n<tbody>\n<tr class=\"oli_table\">\n<td><\/td>\n<td><strong>Arts-Sci<\/strong><\/td>\n<td><strong>Bus-Econ<\/strong><\/td>\n<td><strong>Info Tech<\/strong><\/td>\n<td><strong>Health Science<\/strong><\/td>\n<td><strong>Graphics Design<\/strong><\/td>\n<td><strong>Culinary Arts<\/strong><\/td>\n<td align=\"center\"><strong>Row Totals<\/strong><\/td>\n<\/tr>\n<tr class=\"oli_table\">\n<td align=\"center\"><strong>Female<\/strong><\/td>\n<td align=\"center\">4,660<\/td>\n<td align=\"center\">435<\/td>\n<td align=\"center\">494<\/td>\n<td align=\"center\">421<\/td>\n<td align=\"center\">105<\/td>\n<td align=\"center\">83<\/td>\n<td align=\"center\">6,198<\/td>\n<\/tr>\n<tr class=\"oli_table\">\n<td align=\"center\"><strong>Male<\/strong><\/td>\n<td align=\"center\">4,334<\/td>\n<td align=\"center\">490<\/td>\n<td align=\"center\">564<\/td>\n<td align=\"center\">223<\/td>\n<td align=\"center\">97<\/td>\n<td align=\"center\">94<\/td>\n<td align=\"center\">5,802<\/td>\n<\/tr>\n<tr class=\"oli_table\">\n<td align=\"center\"><strong>Column Totals<\/strong><\/td>\n<td align=\"center\">8,994<\/td>\n<td align=\"center\">925<\/td>\n<td align=\"center\">1,058<\/td>\n<td align=\"center\">644<\/td>\n<td align=\"center\">202<\/td>\n<td align=\"center\">177<\/td>\n<td align=\"center\">12,000<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div class=\"textbox exercises\">\n<h3>Learn By Doing<\/h3>\n<p>\t<iframe id=\"lumen_assessment_3540\" class=\"resizable\" src=\"https:\/\/assessments.lumenlearning.com\/assessments\/load?assessment_id=3540&#38;embed=1&#38;external_user_id=&#38;external_context_id=&#38;iframe_resize_id=lumen_assessment_3540\" frameborder=\"0\" style=\"border:none;width:100%;height:100%;min-height:400px;\"><br \/>\n\t<\/iframe><\/p>\n<p>\t<iframe id=\"lumen_assessment_3541\" class=\"resizable\" src=\"https:\/\/assessments.lumenlearning.com\/assessments\/load?assessment_id=3541&#38;embed=1&#38;external_user_id=&#38;external_context_id=&#38;iframe_resize_id=lumen_assessment_3541\" frameborder=\"0\" style=\"border:none;width:100%;height:100%;min-height:400px;\"><br \/>\n\t<\/iframe><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-253\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Concepts in Statistics. <strong>Provided by<\/strong>: Open Learning Initiative. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/oli.cmu.edu\">http:\/\/oli.cmu.edu<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":163,"menu_order":5,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"Concepts in Statistics\",\"author\":\"\",\"organization\":\"Open Learning Initiative\",\"url\":\"http:\/\/oli.cmu.edu\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"}]","CANDELA_OUTCOMES_GUID":"1069c50d-6e4a-4c0d-ba20-14c8af2cc9db","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-253","chapter","type-chapter","status-web-only","hentry"],"part":245,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/suny-hccc-wm-concepts-statistics\/wp-json\/pressbooks\/v2\/chapters\/253","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/suny-hccc-wm-concepts-statistics\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/suny-hccc-wm-concepts-statistics\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-hccc-wm-concepts-statistics\/wp-json\/wp\/v2\/users\/163"}],"version-history":[{"count":2,"href":"https:\/\/courses.lumenlearning.com\/suny-hccc-wm-concepts-statistics\/wp-json\/pressbooks\/v2\/chapters\/253\/revisions"}],"predecessor-version":[{"id":1382,"href":"https:\/\/courses.lumenlearning.com\/suny-hccc-wm-concepts-statistics\/wp-json\/pressbooks\/v2\/chapters\/253\/revisions\/1382"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/suny-hccc-wm-concepts-statistics\/wp-json\/pressbooks\/v2\/parts\/245"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/suny-hccc-wm-concepts-statistics\/wp-json\/pressbooks\/v2\/chapters\/253\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/suny-hccc-wm-concepts-statistics\/wp-json\/wp\/v2\/media?parent=253"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-hccc-wm-concepts-statistics\/wp-json\/pressbooks\/v2\/chapter-type?post=253"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-hccc-wm-concepts-statistics\/wp-json\/wp\/v2\/contributor?post=253"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-hccc-wm-concepts-statistics\/wp-json\/wp\/v2\/license?post=253"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}