{"id":996,"date":"2023-06-22T01:38:57","date_gmt":"2023-06-22T01:38:57","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/conditional-probabilities-learn-it-2\/"},"modified":"2025-05-11T23:33:19","modified_gmt":"2025-05-11T23:33:19","slug":"conditional-probabilities-learn-it-2","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/conditional-probabilities-learn-it-2\/","title":{"raw":"Conditional Probabilities: Learn It 4","rendered":"Conditional Probabilities: Learn It 4"},"content":{"raw":"<section class=\"textbox learningGoals\">\r\n<ul>\r\n\t<li>Describe and find conditional probabilities.<\/li>\r\n\t<li>Understand the concept of independent events.<\/li>\r\n<\/ul>\r\n<\/section>\r\n<h2>Independent Events<\/h2>\r\n<p>Conditional probabilities provide another way to determine if two events are independent. Remember, independent events are those where the outcome of the first event does not impact the probability of the second event.<\/p>\r\n<section class=\"textbox keyTakeaway\">\r\n<div>\r\n<h3>Independence using conditional probability<\/h3>\r\n<p>Two events [latex]A[\/latex] and [latex]B[\/latex] are independent if\u00a0<\/p>\r\n<ul>\r\n\t<li>[latex]P(A|B)=P(A)[\/latex]<\/li>\r\n\t<li>[latex]P(B|A)=P(B)[\/latex]<\/li>\r\n<\/ul>\r\n<\/div>\r\n<\/section>\r\n<section class=\"textbox recall\">\r\n<p>The other way we identify independent events using probability is by determining if [latex]P(A \\text{ and } B)=P(A)\\cdot P(B)[\/latex]<\/p>\r\n<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]1096[\/ohm2_question]<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]1097[\/ohm2_question]<\/section>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li>Describe and find conditional probabilities.<\/li>\n<li>Understand the concept of independent events.<\/li>\n<\/ul>\n<\/section>\n<h2>Independent Events<\/h2>\n<p>Conditional probabilities provide another way to determine if two events are independent. Remember, independent events are those where the outcome of the first event does not impact the probability of the second event.<\/p>\n<section class=\"textbox keyTakeaway\">\n<div>\n<h3>Independence using conditional probability<\/h3>\n<p>Two events [latex]A[\/latex] and [latex]B[\/latex] are independent if\u00a0<\/p>\n<ul>\n<li>[latex]P(A|B)=P(A)[\/latex]<\/li>\n<li>[latex]P(B|A)=P(B)[\/latex]<\/li>\n<\/ul>\n<\/div>\n<\/section>\n<section class=\"textbox recall\">\n<p>The other way we identify independent events using probability is by determining if [latex]P(A \\text{ and } B)=P(A)\\cdot P(B)[\/latex]<\/p>\n<\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm1096\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=1096&theme=lumen&iframe_resize_id=ohm1096&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm1097\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=1097&theme=lumen&iframe_resize_id=ohm1097&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n","protected":false},"author":8,"menu_order":19,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":974,"module-header":"learn_it","content_attributions":[],"internal_book_links":[],"video_content":null,"cc_video_embed_content":{"cc_scripts":"","media_targets":[]},"try_it_collection":null,"_links":{"self":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/996"}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/users\/8"}],"version-history":[{"count":14,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/996\/revisions"}],"predecessor-version":[{"id":6671,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/996\/revisions\/6671"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/parts\/974"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/996\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=996"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=996"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=996"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=996"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}