{"id":2939,"date":"2019-06-26T05:38:42","date_gmt":"2019-06-26T05:38:42","guid":{"rendered":"https:\/\/analystprep.com\/study-notes\/?p=2939"},"modified":"2026-06-02T20:02:48","modified_gmt":"2026-06-02T20:02:48","slug":"calculate-probabilities-of-mutually-exclusive-events","status":"publish","type":"post","link":"https:\/\/analystprep.com\/study-notes\/actuarial-exams\/soa\/p-probability\/general-probability\/calculate-probabilities-of-mutually-exclusive-events\/","title":{"rendered":"Calculate probabilities of mutually exclusive events"},"content":{"rendered":"<p><script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"ImageObject\",\n  \"url\": \"https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2019\/06\/Mutually-Exclusive-Events-2.jpg\",\n  \"caption\": \"Mutually-Exclusive-Events-2\",\n  \"width\": 1590,\n  \"height\": 1091,\n  \"copyrightNotice\": \"\u00a9 2024 AnalystPrep\",\n  \"acquireLicensePage\": \"https:\/\/analystprep.com\/license-info\",\n  \"creditText\": \"AnalystPrep Design Team\",\n  \"creator\": {\n    \"@type\": \"Organization\",\n    \"name\": \"AnalystPrep\"\n  }\n}\n<\/script><\/p>\n<p><script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"ImageObject\",\n  \"url\": \"https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2019\/06\/Exhaustive-Events.jpg\",\n  \"caption\": \"Exhaustive-Events\",\n  \"width\": 1590,\n  \"height\": 1091,\n  \"copyrightNotice\": \"\u00a9 2024 AnalystPrep\",\n  \"acquireLicensePage\": \"https:\/\/analystprep.com\/license-info\",\n  \"creditText\": \"AnalystPrep Design Team\",\n  \"creator\": {\n    \"@type\": \"Organization\",\n    \"name\": \"AnalystPrep\"\n  }\n}\n<\/script><\/p>\n<h2><strong>Mutually Exclusive Events<\/strong><\/h2>\n<p>\\(A\\) and \\(B\\) are <strong>mutually exclusive<\/strong> events if \\(A\\) and \\(B\\) cannot both occur at the same time. For example, when a coin is flipped, it cannot land on both the head and tail simultaneously. Therefore, we consider the events \u201clanding heads\u201d and \u201clanding tails\u201d as mutually exclusive events.<\/p>\n<p>If events are mutually exclusive, then their intersection \\(\\left( A\\cap B \\right) \\) is equal to \\(\\emptyset\\) (null set).<\/p>\n<p>In the diagram below, \\(A\\) and \\(B\\) are mutually exclusive events.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" width=\"1590\" height=\"1091\" class=\"alignnone size-full wp-image-32399\" style=\"max-width: 100%;\" src=\"https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2019\/06\/Mutually-Exclusive-Events-2.jpg\" alt=\"Mutually Exclusive Events\" srcset=\"https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2019\/06\/Mutually-Exclusive-Events-2.jpg 1590w, https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2019\/06\/Mutually-Exclusive-Events-2-300x206.jpg 300w, https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2019\/06\/Mutually-Exclusive-Events-2-1024x703.jpg 1024w, https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2019\/06\/Mutually-Exclusive-Events-2-768x527.jpg 768w, https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2019\/06\/Mutually-Exclusive-Events-2-1536x1054.jpg 1536w, https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2019\/06\/Mutually-Exclusive-Events-2-400x274.jpg 400w\" sizes=\"auto, (max-width: 1590px) 100vw, 1590px\" \/>If \\(A\\) and \\(B\\) are mutually exclusive, then the probability of \\(A\\) or \\(B\\) occurring is the sum of the probability of event \\(A\\) occurring and the probability of event \\(B\\) occurring, as shown in the formula below:<\/p>\n<p>$$ P(A \\cup B) = P(A) + P(B) $$<\/p>\n<div style=\"margin: 18px 0;\"><a style=\"display: block; text-align: center; padding: 14px 18px; border: 2px solid #2F5BFF; border-radius: 18px; color: #ffffff; font-weight: 600; font-size: 16px; text-decoration: none; background-color: #1a73e8;\" href=\"https:\/\/analystprep.com\/free-trial\/\" target=\"_blank\" rel=\"noopener noreferrer\">Strengthen your SOA Exam P probability concepts with our Free Trial.<\/a><\/div>\n<h3><strong>Example: Mutually Exclusive Events<\/strong><\/h3>\n<p>Consider drawing 2 cards from a standard deck. Let event \\(A\\) be drawing a Jack and event \\(B\\) be drawing a Queen. The probability of event \\(A\\) occurring is \\({4}\/{52}\\) or \\({1}\/{13}\\) and the probability of event \\(B\\) is also \\({4}\/{52}\\) or \\({1}\/{13}\\). Therefore, we can calculate:<\/p>\n<p>$$ P(A\\cup B)=P(A)+P(B)={ 1 }\/{ 13 }+{ 1 }\/{ 13 }=2\/{ 13 } $$<\/p>\n<p>Events \\(A\\) and \\(B\\) are <strong>exhaustive<\/strong> events if \\(A\\cup B\\) is equal to the entire sample space, \\(S\\). It follows then that if \\(A\\) and \\(B\\) are mutually exclusive and exhaustive events then \\(A\\cap B=\\emptyset \\) and \\(A\\cup B=S\\).<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" width=\"1590\" height=\"1091\" class=\"alignnone size-full wp-image-32400\" src=\"https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2019\/06\/Exhaustive-Events.jpg\" alt=\"Exhaustive Events\" style=\"max-width:100%\" srcset=\"https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2019\/06\/Exhaustive-Events.jpg 1590w, https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2019\/06\/Exhaustive-Events-300x206.jpg 300w, https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2019\/06\/Exhaustive-Events-1024x703.jpg 1024w, https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2019\/06\/Exhaustive-Events-768x527.jpg 768w, https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2019\/06\/Exhaustive-Events-1536x1054.jpg 1536w, https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2019\/06\/Exhaustive-Events-400x274.jpg 400w\" sizes=\"auto, (max-width: 1590px) 100vw, 1590px\" \/>Consider event \\(A\\) and its\u00a0 complement\u00a0 \\(A^{c}\\) (or \\(A^{\\prime}\\)). These events are mutually exclusive and because they make up the entire sample space, \\(S\\), they are also exhaustive. Therefore,<\/p>\n<p>$$ \\begin{align*} &amp; P\\left( A \\right) +P\\left( { A }^{ \u2019 } \\right) =1,\\quad \\text{and} \\\\ &amp; P\\left( A \\right) =1-P\\left( { A }^{ \u2019 } \\right) \\\\ \\end{align*} $$<\/p>\n<h3 style=\"text-align: left;\"><strong>Example: Mutually Exclusive Events<\/strong><\/h3>\n<p>Consider the experiment rolling a 6-sided die until a 1 is rolled. If we define event \\(A\\) as \u201cNOT rolling a 1 before the 3<sup>rd<\/sup> roll,\u201d then we can define event A\u2019 as \u201crolling a 1 before the 3<sup>rd<\/sup> roll\u201d which is the same as rolling a 1 on either the 1<sup>st<\/sup> or 2<sup>nd<\/sup> roll.<\/p>\n<p>The probability of rolling a 1 on the 1<sup>st<\/sup> roll is \\({1}\/{6}\\).<\/p>\n<p>The probability of rolling a 1 on the 2<sup>nd<\/sup> roll is \\({5}\/{6}\\) (because if we rolled a 1 on the 1<sup>st<\/sup> roll we would have stopped) * \\({1}\/{6}\\) = \\({5}\/{36}\\)<\/p>\n<p>$$ \\begin{align*} &amp; P\\left( { A }^{ \u2019 } \\right) ={ 1 }\/{ 6 }+{ 5 }\/{ 36 }={ 11 }\/{ 36 } \\\\ &amp; P\\left( A \\right) =1-P\\left( { A }^{ \u2019 } \\right) =1-{ 11 }\/{ 36 }={ 25 }\/{ 36 } \\\\ \\end{align*} $$<\/p>\n<p><em><strong>Learning Outcome<\/strong><\/em><\/p>\n<p><em><strong>1.d Topic: General Probability &#8211;\u00a0Calculate probabilities of mutually exclusive events.\u00a0<\/strong><\/em><\/p>\n<div style=\"text-align: center; margin: 30px 0;\"><a style=\"display: inline-flex; align-items: center; justify-content: center; padding: 12px 26px; border-radius: 9999px; background: #1e5bd8; color: #ffffff; font-weight: bold; text-decoration: none;\" href=\"https:\/\/analystprep.com\/free-trial\/\" target=\"_blank\" rel=\"noopener noreferrer\"> Start Free Trial \u2192 <\/a><\/p>\n<p style=\"margin-top: 12px; font-size: 16px; line-height: 1.5;\">Access SOA Exam P probability study notes, practice questions, mock exams, and video lessons to strengthen your understanding of mutually exclusive events and probability calculations.<\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Mutually Exclusive Events \\(A\\) and \\(B\\) are mutually exclusive events if \\(A\\) and \\(B\\) cannot both occur at the same time. For example, when a coin is flipped, it cannot land on both the head and tail simultaneously. Therefore, we&#8230;<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[97],"tags":[],"class_list":["post-2939","post","type-post","status-publish","format-standard","hentry","category-general-probability","blog-post","no-post-thumbnail","animate"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.6 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Mutually Exclusive Events | AnalystPrep<\/title>\n<meta name=\"description\" content=\"Learn how to calculate probabilities of mutually exclusive events and apply key probability rules with examples.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/analystprep.com\/study-notes\/actuarial-exams\/soa\/p-probability\/general-probability\/calculate-probabilities-of-mutually-exclusive-events\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Mutually Exclusive Events | AnalystPrep\" \/>\n<meta property=\"og:description\" content=\"Learn how to calculate probabilities of mutually exclusive events and apply key probability rules with examples.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/analystprep.com\/study-notes\/actuarial-exams\/soa\/p-probability\/general-probability\/calculate-probabilities-of-mutually-exclusive-events\/\" \/>\n<meta property=\"og:site_name\" content=\"CFA, FRM, and Actuarial Exams Study Notes\" \/>\n<meta property=\"article:published_time\" content=\"2019-06-26T05:38:42+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2026-06-02T20:02:48+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2019\/06\/Mutually-Exclusive-Events-2.jpg\" \/>\n\t<meta property=\"og:image:width\" content=\"1590\" \/>\n\t<meta property=\"og:image:height\" content=\"1091\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/jpeg\" \/>\n<meta name=\"author\" content=\"Jasmine Keizer\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"Jasmine Keizer\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"3 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\\\/\\\/analystprep.com\\\/study-notes\\\/actuarial-exams\\\/soa\\\/p-probability\\\/general-probability\\\/calculate-probabilities-of-mutually-exclusive-events\\\/#article\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/analystprep.com\\\/study-notes\\\/actuarial-exams\\\/soa\\\/p-probability\\\/general-probability\\\/calculate-probabilities-of-mutually-exclusive-events\\\/\"},\"author\":{\"name\":\"Jasmine Keizer\",\"@id\":\"https:\\\/\\\/analystprep.com\\\/study-notes\\\/#\\\/schema\\\/person\\\/2280b3ab50717cffd45a0f28f27eb6b5\"},\"headline\":\"Calculate probabilities of mutually exclusive events\",\"datePublished\":\"2019-06-26T05:38:42+00:00\",\"dateModified\":\"2026-06-02T20:02:48+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\\\/\\\/analystprep.com\\\/study-notes\\\/actuarial-exams\\\/soa\\\/p-probability\\\/general-probability\\\/calculate-probabilities-of-mutually-exclusive-events\\\/\"},\"wordCount\":446,\"image\":{\"@id\":\"https:\\\/\\\/analystprep.com\\\/study-notes\\\/actuarial-exams\\\/soa\\\/p-probability\\\/general-probability\\\/calculate-probabilities-of-mutually-exclusive-events\\\/#primaryimage\"},\"thumbnailUrl\":\"https:\\\/\\\/analystprep.com\\\/study-notes\\\/wp-content\\\/uploads\\\/2019\\\/06\\\/Mutually-Exclusive-Events-2.jpg\",\"articleSection\":[\"General Probability\"],\"inLanguage\":\"en-US\"},{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/analystprep.com\\\/study-notes\\\/actuarial-exams\\\/soa\\\/p-probability\\\/general-probability\\\/calculate-probabilities-of-mutually-exclusive-events\\\/\",\"url\":\"https:\\\/\\\/analystprep.com\\\/study-notes\\\/actuarial-exams\\\/soa\\\/p-probability\\\/general-probability\\\/calculate-probabilities-of-mutually-exclusive-events\\\/\",\"name\":\"Mutually Exclusive Events | AnalystPrep\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/analystprep.com\\\/study-notes\\\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\\\/\\\/analystprep.com\\\/study-notes\\\/actuarial-exams\\\/soa\\\/p-probability\\\/general-probability\\\/calculate-probabilities-of-mutually-exclusive-events\\\/#primaryimage\"},\"image\":{\"@id\":\"https:\\\/\\\/analystprep.com\\\/study-notes\\\/actuarial-exams\\\/soa\\\/p-probability\\\/general-probability\\\/calculate-probabilities-of-mutually-exclusive-events\\\/#primaryimage\"},\"thumbnailUrl\":\"https:\\\/\\\/analystprep.com\\\/study-notes\\\/wp-content\\\/uploads\\\/2019\\\/06\\\/Mutually-Exclusive-Events-2.jpg\",\"datePublished\":\"2019-06-26T05:38:42+00:00\",\"dateModified\":\"2026-06-02T20:02:48+00:00\",\"author\":{\"@id\":\"https:\\\/\\\/analystprep.com\\\/study-notes\\\/#\\\/schema\\\/person\\\/2280b3ab50717cffd45a0f28f27eb6b5\"},\"description\":\"Learn how to calculate probabilities of mutually exclusive events and apply key probability rules with examples.\",\"breadcrumb\":{\"@id\":\"https:\\\/\\\/analystprep.com\\\/study-notes\\\/actuarial-exams\\\/soa\\\/p-probability\\\/general-probability\\\/calculate-probabilities-of-mutually-exclusive-events\\\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\\\/\\\/analystprep.com\\\/study-notes\\\/actuarial-exams\\\/soa\\\/p-probability\\\/general-probability\\\/calculate-probabilities-of-mutually-exclusive-events\\\/\"]}]},{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\\\/\\\/analystprep.com\\\/study-notes\\\/actuarial-exams\\\/soa\\\/p-probability\\\/general-probability\\\/calculate-probabilities-of-mutually-exclusive-events\\\/#primaryimage\",\"url\":\"https:\\\/\\\/analystprep.com\\\/study-notes\\\/wp-content\\\/uploads\\\/2019\\\/06\\\/Mutually-Exclusive-Events-2.jpg\",\"contentUrl\":\"https:\\\/\\\/analystprep.com\\\/study-notes\\\/wp-content\\\/uploads\\\/2019\\\/06\\\/Mutually-Exclusive-Events-2.jpg\",\"width\":1590,\"height\":1091,\"caption\":\"Mutually Exclusive Events\"},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\\\/\\\/analystprep.com\\\/study-notes\\\/actuarial-exams\\\/soa\\\/p-probability\\\/general-probability\\\/calculate-probabilities-of-mutually-exclusive-events\\\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\\\/\\\/analystprep.com\\\/study-notes\\\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Calculate probabilities of mutually exclusive events\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\\\/\\\/analystprep.com\\\/study-notes\\\/#website\",\"url\":\"https:\\\/\\\/analystprep.com\\\/study-notes\\\/\",\"name\":\"CFA, FRM, and Actuarial Exams Study Notes\",\"description\":\"Question Bank and Study Notes for the CFA, FRM, and Actuarial exams\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\\\/\\\/analystprep.com\\\/study-notes\\\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"en-US\"},{\"@type\":\"Person\",\"@id\":\"https:\\\/\\\/analystprep.com\\\/study-notes\\\/#\\\/schema\\\/person\\\/2280b3ab50717cffd45a0f28f27eb6b5\",\"name\":\"Jasmine Keizer\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\\\/\\\/secure.gravatar.com\\\/avatar\\\/6d6cbbbd1d0c7637649aa2a266d4b93d5b354480307d29433711b664817e0497?s=96&d=mm&r=g\",\"url\":\"https:\\\/\\\/secure.gravatar.com\\\/avatar\\\/6d6cbbbd1d0c7637649aa2a266d4b93d5b354480307d29433711b664817e0497?s=96&d=mm&r=g\",\"contentUrl\":\"https:\\\/\\\/secure.gravatar.com\\\/avatar\\\/6d6cbbbd1d0c7637649aa2a266d4b93d5b354480307d29433711b664817e0497?s=96&d=mm&r=g\",\"caption\":\"Jasmine Keizer\"},\"url\":\"https:\\\/\\\/analystprep.com\\\/study-notes\\\/author\\\/admin\\\/\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Mutually Exclusive Events | AnalystPrep","description":"Learn how to calculate probabilities of mutually exclusive events and apply key probability rules with examples.","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/analystprep.com\/study-notes\/actuarial-exams\/soa\/p-probability\/general-probability\/calculate-probabilities-of-mutually-exclusive-events\/","og_locale":"en_US","og_type":"article","og_title":"Mutually Exclusive Events | AnalystPrep","og_description":"Learn how to calculate probabilities of mutually exclusive events and apply key probability rules with examples.","og_url":"https:\/\/analystprep.com\/study-notes\/actuarial-exams\/soa\/p-probability\/general-probability\/calculate-probabilities-of-mutually-exclusive-events\/","og_site_name":"CFA, FRM, and Actuarial Exams Study Notes","article_published_time":"2019-06-26T05:38:42+00:00","article_modified_time":"2026-06-02T20:02:48+00:00","og_image":[{"width":1590,"height":1091,"url":"https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2019\/06\/Mutually-Exclusive-Events-2.jpg","type":"image\/jpeg"}],"author":"Jasmine Keizer","twitter_card":"summary_large_image","twitter_misc":{"Written by":"Jasmine Keizer","Est. reading time":"3 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/analystprep.com\/study-notes\/actuarial-exams\/soa\/p-probability\/general-probability\/calculate-probabilities-of-mutually-exclusive-events\/#article","isPartOf":{"@id":"https:\/\/analystprep.com\/study-notes\/actuarial-exams\/soa\/p-probability\/general-probability\/calculate-probabilities-of-mutually-exclusive-events\/"},"author":{"name":"Jasmine Keizer","@id":"https:\/\/analystprep.com\/study-notes\/#\/schema\/person\/2280b3ab50717cffd45a0f28f27eb6b5"},"headline":"Calculate probabilities of mutually exclusive events","datePublished":"2019-06-26T05:38:42+00:00","dateModified":"2026-06-02T20:02:48+00:00","mainEntityOfPage":{"@id":"https:\/\/analystprep.com\/study-notes\/actuarial-exams\/soa\/p-probability\/general-probability\/calculate-probabilities-of-mutually-exclusive-events\/"},"wordCount":446,"image":{"@id":"https:\/\/analystprep.com\/study-notes\/actuarial-exams\/soa\/p-probability\/general-probability\/calculate-probabilities-of-mutually-exclusive-events\/#primaryimage"},"thumbnailUrl":"https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2019\/06\/Mutually-Exclusive-Events-2.jpg","articleSection":["General Probability"],"inLanguage":"en-US"},{"@type":"WebPage","@id":"https:\/\/analystprep.com\/study-notes\/actuarial-exams\/soa\/p-probability\/general-probability\/calculate-probabilities-of-mutually-exclusive-events\/","url":"https:\/\/analystprep.com\/study-notes\/actuarial-exams\/soa\/p-probability\/general-probability\/calculate-probabilities-of-mutually-exclusive-events\/","name":"Mutually Exclusive Events | AnalystPrep","isPartOf":{"@id":"https:\/\/analystprep.com\/study-notes\/#website"},"primaryImageOfPage":{"@id":"https:\/\/analystprep.com\/study-notes\/actuarial-exams\/soa\/p-probability\/general-probability\/calculate-probabilities-of-mutually-exclusive-events\/#primaryimage"},"image":{"@id":"https:\/\/analystprep.com\/study-notes\/actuarial-exams\/soa\/p-probability\/general-probability\/calculate-probabilities-of-mutually-exclusive-events\/#primaryimage"},"thumbnailUrl":"https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2019\/06\/Mutually-Exclusive-Events-2.jpg","datePublished":"2019-06-26T05:38:42+00:00","dateModified":"2026-06-02T20:02:48+00:00","author":{"@id":"https:\/\/analystprep.com\/study-notes\/#\/schema\/person\/2280b3ab50717cffd45a0f28f27eb6b5"},"description":"Learn how to calculate probabilities of mutually exclusive events and apply key probability rules with examples.","breadcrumb":{"@id":"https:\/\/analystprep.com\/study-notes\/actuarial-exams\/soa\/p-probability\/general-probability\/calculate-probabilities-of-mutually-exclusive-events\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/analystprep.com\/study-notes\/actuarial-exams\/soa\/p-probability\/general-probability\/calculate-probabilities-of-mutually-exclusive-events\/"]}]},{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/analystprep.com\/study-notes\/actuarial-exams\/soa\/p-probability\/general-probability\/calculate-probabilities-of-mutually-exclusive-events\/#primaryimage","url":"https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2019\/06\/Mutually-Exclusive-Events-2.jpg","contentUrl":"https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2019\/06\/Mutually-Exclusive-Events-2.jpg","width":1590,"height":1091,"caption":"Mutually Exclusive Events"},{"@type":"BreadcrumbList","@id":"https:\/\/analystprep.com\/study-notes\/actuarial-exams\/soa\/p-probability\/general-probability\/calculate-probabilities-of-mutually-exclusive-events\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/analystprep.com\/study-notes\/"},{"@type":"ListItem","position":2,"name":"Calculate probabilities of mutually exclusive events"}]},{"@type":"WebSite","@id":"https:\/\/analystprep.com\/study-notes\/#website","url":"https:\/\/analystprep.com\/study-notes\/","name":"CFA, FRM, and Actuarial Exams Study Notes","description":"Question Bank and Study Notes for the CFA, FRM, and Actuarial exams","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/analystprep.com\/study-notes\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"en-US"},{"@type":"Person","@id":"https:\/\/analystprep.com\/study-notes\/#\/schema\/person\/2280b3ab50717cffd45a0f28f27eb6b5","name":"Jasmine Keizer","image":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/secure.gravatar.com\/avatar\/6d6cbbbd1d0c7637649aa2a266d4b93d5b354480307d29433711b664817e0497?s=96&d=mm&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/6d6cbbbd1d0c7637649aa2a266d4b93d5b354480307d29433711b664817e0497?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/6d6cbbbd1d0c7637649aa2a266d4b93d5b354480307d29433711b664817e0497?s=96&d=mm&r=g","caption":"Jasmine Keizer"},"url":"https:\/\/analystprep.com\/study-notes\/author\/admin\/"}]}},"_links":{"self":[{"href":"https:\/\/analystprep.com\/study-notes\/wp-json\/wp\/v2\/posts\/2939","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/analystprep.com\/study-notes\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/analystprep.com\/study-notes\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/analystprep.com\/study-notes\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/analystprep.com\/study-notes\/wp-json\/wp\/v2\/comments?post=2939"}],"version-history":[{"count":16,"href":"https:\/\/analystprep.com\/study-notes\/wp-json\/wp\/v2\/posts\/2939\/revisions"}],"predecessor-version":[{"id":43767,"href":"https:\/\/analystprep.com\/study-notes\/wp-json\/wp\/v2\/posts\/2939\/revisions\/43767"}],"wp:attachment":[{"href":"https:\/\/analystprep.com\/study-notes\/wp-json\/wp\/v2\/media?parent=2939"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/analystprep.com\/study-notes\/wp-json\/wp\/v2\/categories?post=2939"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/analystprep.com\/study-notes\/wp-json\/wp\/v2\/tags?post=2939"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}