{"id":987,"date":"2023-06-22T01:38:50","date_gmt":"2023-06-22T01:38:50","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/probabilities-of-two-events-learn-it-1\/"},"modified":"2025-05-10T22:31:49","modified_gmt":"2025-05-10T22:31:49","slug":"probabilities-of-two-events-learn-it-1","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/probabilities-of-two-events-learn-it-1\/","title":{"raw":"Probability of Compound Events: Learn It 1","rendered":"Probability of Compound Events: Learn It 1"},"content":{"raw":"<section class=\"textbox learningGoals\">\r\n<ul>\r\n\t<li>Calculate and interpret probabilities of simple and compound events.<\/li>\r\n\t<li>Describe the meaning of mutually exclusive and independence using probability.<\/li>\r\n<\/ul>\r\n<\/section>\r\n<section class=\"textbox recall\">[latex]P(\\text{event}) = \\dfrac{\\text{number of outcomes in event}}{\\text{number of all possible outcomes}}[\/latex] <br \/>\r\n<br \/>\r\n<strong>Facts about probabilities: <\/strong>\r\n<ul>\r\n\t<li>The probability of a <strong>certain event<\/strong> (an event that will happen) is equal to [latex]1[\/latex].<\/li>\r\n\t<li>The probability of an <strong>impossible event<\/strong> is equal to [latex]0[\/latex]. This means that there are no possible outcomes for that event.<\/li>\r\n\t<li>Probabilities range from [latex]0[\/latex] to [latex]1[\/latex], including [latex]0[\/latex] and [latex]1[\/latex]. So, for any event [latex]\\text{A}[\/latex], [latex]0\\leq P(\\text{A})\\leq1[\/latex].<\/li>\r\n\t<li><span style=\"font-size: 1em;\">Probabilities can be expressed as decimals, fractions, or percentages.<\/span><\/li>\r\n<\/ul>\r\n<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]1086[\/ohm2_question]<\/section>\r\n<section class=\"textbox proTip\">The\u00a0<strong>sample space<\/strong>\u00a0of an experiment is the set of all possible outcomes. Because the sample space consists of all of the outcomes,\u00a0[latex]P(\\text{sample space}) = 1 = 100\\%[\/latex].<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]1417[\/ohm2_question]<\/section>\r\n<h2>Complement of an Event<\/h2>\r\n<p>The\u00a0<strong>complement<\/strong> of event [latex]A[\/latex] is denoted [latex]A'[\/latex] (read \"[latex]A[\/latex] prime\") or [latex]A^c[\/latex] (read \"[latex]A[\/latex] complement\"). The complement of the event [latex]A[\/latex] consists of all outcomes that are <strong>NOT<\/strong> in [latex]A[\/latex].<\/p>\r\n<p>More generally, for any event [latex]A[\/latex], we can think of the probability of complements as having the following relationship:<\/p>\r\n<p style=\"text-align: center;\">[latex]P[\/latex]([latex]A[\/latex]) + [latex]P[\/latex](not [latex]A[\/latex]) = [latex]1[\/latex]<\/p>\r\n<p style=\"text-align: center;\">or<\/p>\r\n<p style=\"text-align: center;\">[latex]P[\/latex]([latex]A[\/latex]) + [latex]P[\/latex]([latex]A'[\/latex]) = [latex]1[\/latex]<\/p>\r\n<p>The equation can also be rewritten as follows:\u00a0[latex]P[\/latex](not [latex]A[\/latex]) = [latex]1[\/latex] - [latex]P[\/latex]([latex]A[\/latex])<\/p>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]1087[\/ohm2_question]<\/section>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li>Calculate and interpret probabilities of simple and compound events.<\/li>\n<li>Describe the meaning of mutually exclusive and independence using probability.<\/li>\n<\/ul>\n<\/section>\n<section class=\"textbox recall\">[latex]P(\\text{event}) = \\dfrac{\\text{number of outcomes in event}}{\\text{number of all possible outcomes}}[\/latex] <\/p>\n<p><strong>Facts about probabilities: <\/strong><\/p>\n<ul>\n<li>The probability of a <strong>certain event<\/strong> (an event that will happen) is equal to [latex]1[\/latex].<\/li>\n<li>The probability of an <strong>impossible event<\/strong> is equal to [latex]0[\/latex]. This means that there are no possible outcomes for that event.<\/li>\n<li>Probabilities range from [latex]0[\/latex] to [latex]1[\/latex], including [latex]0[\/latex] and [latex]1[\/latex]. So, for any event [latex]\\text{A}[\/latex], [latex]0\\leq P(\\text{A})\\leq1[\/latex].<\/li>\n<li><span style=\"font-size: 1em;\">Probabilities can be expressed as decimals, fractions, or percentages.<\/span><\/li>\n<\/ul>\n<\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm1086\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=1086&theme=lumen&iframe_resize_id=ohm1086&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox proTip\">The\u00a0<strong>sample space<\/strong>\u00a0of an experiment is the set of all possible outcomes. Because the sample space consists of all of the outcomes,\u00a0[latex]P(\\text{sample space}) = 1 = 100\\%[\/latex].<\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm1417\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=1417&theme=lumen&iframe_resize_id=ohm1417&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<h2>Complement of an Event<\/h2>\n<p>The\u00a0<strong>complement<\/strong> of event [latex]A[\/latex] is denoted [latex]A'[\/latex] (read &#8220;[latex]A[\/latex] prime&#8221;) or [latex]A^c[\/latex] (read &#8220;[latex]A[\/latex] complement&#8221;). The complement of the event [latex]A[\/latex] consists of all outcomes that are <strong>NOT<\/strong> in [latex]A[\/latex].<\/p>\n<p>More generally, for any event [latex]A[\/latex], we can think of the probability of complements as having the following relationship:<\/p>\n<p style=\"text-align: center;\">[latex]P[\/latex]([latex]A[\/latex]) + [latex]P[\/latex](not [latex]A[\/latex]) = [latex]1[\/latex]<\/p>\n<p style=\"text-align: center;\">or<\/p>\n<p style=\"text-align: center;\">[latex]P[\/latex]([latex]A[\/latex]) + [latex]P[\/latex]([latex]A'[\/latex]) = [latex]1[\/latex]<\/p>\n<p>The equation can also be rewritten as follows:\u00a0[latex]P[\/latex](not [latex]A[\/latex]) = [latex]1[\/latex] &#8211; [latex]P[\/latex]([latex]A[\/latex])<\/p>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm1087\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=1087&theme=lumen&iframe_resize_id=ohm1087&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n","protected":false},"author":8,"menu_order":10,"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\/987"}],"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":12,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/987\/revisions"}],"predecessor-version":[{"id":6536,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/987\/revisions\/6536"}],"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\/987\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=987"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=987"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=987"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=987"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}