{"id":2689,"date":"2021-11-12T12:52:52","date_gmt":"2021-11-12T12:52:52","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/?post_type=chapter&#038;p=2689"},"modified":"2023-12-05T09:05:46","modified_gmt":"2023-12-05T09:05:46","slug":"putting-it-together-probability-topics","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/chapter\/putting-it-together-probability-topics\/","title":{"raw":"Putting It Together: Probability Topics","rendered":"Putting It Together: Probability Topics"},"content":{"raw":"<h2>Let\u2019s Summarize<\/h2>\r\nTo summarize the relationship between two categorical variables, use:\r\n<ul>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">Data display: contingency table, tree diagram or Venn diagram<\/li>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">Numerical summaries: probabilities<\/li>\r\n<\/ul>\r\n<h2>Keys Ideas from Our Work with Probability<\/h2>\r\n<ul>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">The <em>probability<\/em> of an event is a measure of the likelihood that the event occurs. Probabilities are always between [latex]0[\/latex] and [latex]1[\/latex]. The closer the probability is to [latex]0[\/latex], the less likely the event is to occur. The closer the probability is to [latex]1[\/latex], the more likely the event is to occur.<\/li>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">A sample space or contingency tables can be used to calculate basic probabilities, where you count the number of items of interest and divide by the total number of items.<\/li>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">[latex]P(A \\ \\mathrm{and} \\ B)[\/latex] means events [latex]A[\/latex] and [latex]B[\/latex] must happen in the same outcome. If [latex]A[\/latex] and [latex]B[\/latex] are independent events, then [latex]P(A \\ \\mathrm{and} \\ B) = P(A)P(B)[\/latex].<\/li>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">[latex]P(A \\ \\mathrm{or} \\ B)[\/latex] means either event [latex]A[\/latex] or [latex]B[\/latex] (or both) must happen in the outcome.\r\n<ul>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"2\">If [latex]A[\/latex] and [latex]B[\/latex] are any two mutually exclusive events, then [latex]P(A \\ \\mathrm{OR} \\ B) = P(A) + P(B)[\/latex].<\/li>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"2\">If [latex]A[\/latex] and [latex]B[\/latex] are NOT mutually exclusive events, then [latex]P(A \\ \\mathrm{OR} \\ B) = P(A) + P(B) - P(A \\ \\mathrm{and} \\ B)[\/latex].<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">A conditional probability is calculated based on the assumption that one event has already occurred. A conditional probability for event [latex]A[\/latex] given event [latex]B[\/latex] has happened is calculated as: [latex]P(A|B) = \\frac{P(A \\ \\mathrm{and} \\ B)}{P(B)}[\/latex]<\/li>\r\n<\/ul>","rendered":"<h2>Let\u2019s Summarize<\/h2>\n<p>To summarize the relationship between two categorical variables, use:<\/p>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\">Data display: contingency table, tree diagram or Venn diagram<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\">Numerical summaries: probabilities<\/li>\n<\/ul>\n<h2>Keys Ideas from Our Work with Probability<\/h2>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\">The <em>probability<\/em> of an event is a measure of the likelihood that the event occurs. Probabilities are always between [latex]0[\/latex] and [latex]1[\/latex]. The closer the probability is to [latex]0[\/latex], the less likely the event is to occur. The closer the probability is to [latex]1[\/latex], the more likely the event is to occur.<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\">A sample space or contingency tables can be used to calculate basic probabilities, where you count the number of items of interest and divide by the total number of items.<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\">[latex]P(A \\ \\mathrm{and} \\ B)[\/latex] means events [latex]A[\/latex] and [latex]B[\/latex] must happen in the same outcome. If [latex]A[\/latex] and [latex]B[\/latex] are independent events, then [latex]P(A \\ \\mathrm{and} \\ B) = P(A)P(B)[\/latex].<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\">[latex]P(A \\ \\mathrm{or} \\ B)[\/latex] means either event [latex]A[\/latex] or [latex]B[\/latex] (or both) must happen in the outcome.\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"2\">If [latex]A[\/latex] and [latex]B[\/latex] are any two mutually exclusive events, then [latex]P(A \\ \\mathrm{OR} \\ B) = P(A) + P(B)[\/latex].<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"2\">If [latex]A[\/latex] and [latex]B[\/latex] are NOT mutually exclusive events, then [latex]P(A \\ \\mathrm{OR} \\ B) = P(A) + P(B) - P(A \\ \\mathrm{and} \\ B)[\/latex].<\/li>\n<\/ul>\n<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\">A conditional probability is calculated based on the assumption that one event has already occurred. A conditional probability for event [latex]A[\/latex] given event [latex]B[\/latex] has happened is calculated as: [latex]P(A|B) = \\frac{P(A \\ \\mathrm{and} \\ B)}{P(B)}[\/latex]<\/li>\n<\/ul>\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-2689\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Original<\/div><ul class=\"citation-list\"><li><strong>Provided by<\/strong>: Lumen Learning. <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 class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Introductory Statistics. <strong>Authored by<\/strong>: Barbara Illowsky, Susan Dean. <strong>Provided by<\/strong>: Open Stax. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/openstax.org\/books\/introductory-statistics\/pages\/1-introduction\">https:\/\/openstax.org\/books\/introductory-statistics\/pages\/1-introduction<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: Access for free at https:\/\/openstax.org\/books\/introductory-statistics\/pages\/1-introduction<\/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":169134,"menu_order":24,"template":"","meta":{"_candela_citation":"[{\"type\":\"original\",\"description\":\"\",\"author\":\"\",\"organization\":\"Lumen Learning\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Introductory Statistics\",\"author\":\"Barbara Illowsky, Susan Dean\",\"organization\":\"Open Stax\",\"url\":\"https:\/\/openstax.org\/books\/introductory-statistics\/pages\/1-introduction\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Access for free at https:\/\/openstax.org\/books\/introductory-statistics\/pages\/1-introduction\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-2689","chapter","type-chapter","status-publish","hentry"],"part":43,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/2689","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/users\/169134"}],"version-history":[{"count":9,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/2689\/revisions"}],"predecessor-version":[{"id":2698,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/2689\/revisions\/2698"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/parts\/43"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/2689\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/media?parent=2689"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapter-type?post=2689"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/contributor?post=2689"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/license?post=2689"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}