{"id":1159,"date":"2021-08-19T18:36:05","date_gmt":"2021-08-19T18:36:05","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/?post_type=chapter&#038;p=1159"},"modified":"2023-12-05T09:02:54","modified_gmt":"2023-12-05T09:02:54","slug":"summary-two-basic-rules-of-probability","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/chapter\/summary-two-basic-rules-of-probability\/","title":{"raw":"Summary: Two Basic Rules of Probability","rendered":"Summary: Two Basic Rules of Probability"},"content":{"raw":"<h2>Key Concepts<\/h2>\r\n<ul>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">If two events are mutually exclusive, the addition rule for probability can be used to determine the probability of the outcome.<\/li>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">If two events are not mutually exclusive, the addition rule for probability needs to be modified to determine the probability of the outcome.<\/li>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">If two events are independent, the multiplication rule for probability can be used to determine the probability of the outcome.<\/li>\r\n<\/ul>\r\n<h2>Glossary<\/h2>\r\n<strong>addition rule for probability: <\/strong>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]. 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].\r\n\r\n<strong>multiplication rule for probability:\u00a0<\/strong>if\u00a0[latex]A[\/latex] and [latex]B[\/latex] are independent events, then [latex]P(A \\ \\mathrm{and} \\ B) = P(A)P(B)[\/latex]\r\n\r\n<strong>sample space\u00a0<\/strong>the set of all possible outcomes of an experiment","rendered":"<h2>Key Concepts<\/h2>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\">If two events are mutually exclusive, the addition rule for probability can be used to determine the probability of the outcome.<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\">If two events are not mutually exclusive, the addition rule for probability needs to be modified to determine the probability of the outcome.<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\">If two events are independent, the multiplication rule for probability can be used to determine the probability of the outcome.<\/li>\n<\/ul>\n<h2>Glossary<\/h2>\n<p><strong>addition rule for probability: <\/strong>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]. 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].<\/p>\n<p><strong>multiplication rule for probability:\u00a0<\/strong>if\u00a0[latex]A[\/latex] and [latex]B[\/latex] are independent events, then [latex]P(A \\ \\mathrm{and} \\ B) = P(A)P(B)[\/latex]<\/p>\n<p><strong>sample space\u00a0<\/strong>the set of all possible outcomes of an experiment<\/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-1159\">\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\/3-key-terms\">https:\/\/openstax.org\/books\/introductory-statistics\/pages\/3-key-terms<\/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":16,"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\/3-key-terms\",\"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-1159","chapter","type-chapter","status-publish","hentry"],"part":43,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/1159","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":4,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/1159\/revisions"}],"predecessor-version":[{"id":3512,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/1159\/revisions\/3512"}],"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\/1159\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/media?parent=1159"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapter-type?post=1159"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/contributor?post=1159"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/license?post=1159"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}