{"id":2366,"date":"2012-11-14T03:56:30","date_gmt":"2012-11-14T03:56:30","guid":{"rendered":"http:\/\/testpreparations.com\/help\/?p=2366"},"modified":"2014-12-02T08:31:56","modified_gmt":"2014-12-02T08:31:56","slug":"introduction-to-probability-mutually-exclusive-events","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/help\/introduction-to-probability-mutually-exclusive-events\/","title":{"rendered":"Introduction to Probability: Mutually Exclusive Events"},"content":{"rendered":"<p>Two events are <strong>mutually exclusive<\/strong> if they cannot occur simultaneously.<\/p>\n<p>Here are some examples of events which are mutually exclusive:<\/p>\n<ul>\n<li>Turning left and turning right are mutually exclusive because you cannot do both at the same time<\/li>\n<li>When you toss a coin, landing on heads or tails are mutually exclusive events<\/li>\n<li>When choosing a single card, picking a King and an Ace are mutually exclusive<\/li>\n<\/ul>\n<p>Here are some examples of events which are not mutually exclusive:<\/p>\n<ul>\n<li>Turning left and scratching your head can happen at the same time<\/li>\n<li>When choosing a single card; picking a King and a Heart are not mutually exclusive because you can pick a King of Hearts<\/li>\n<\/ul>\n<p>When two events, A and B, are mutually exclusive it is impossible for them to happen together:<\/p>\n<p><span style=\"color: #ffffff\">______<\/span>P(A and B) = 0<\/p>\n<p><span style=\"color: #ffffff\">______<\/span>\u201cthe probability of A and B happening together equals 0\u201d<\/p>\n<p>The probability of A or B is the sum of the individual probabilities:<\/p>\n<p><span style=\"color: #ffffff\">______<\/span>P(A or B) = P(A) + P(B)<\/p>\n<p><span style=\"color: #ffffff\">______<\/span>\u201cthe probability of A or B equals the probability of A plus the probability of B\u201d.<\/p>\n<p>&nbsp;<\/p>\n<p><strong>Example:<\/strong> A Deck of Cards<\/p>\n<p>In a deck of 52 Cards:<\/p>\n<p><span style=\"color: #ffffff\">______<\/span>The probability of selecting a King is 1\/13, so P(King) = 1\/13<\/p>\n<p><span style=\"color: #ffffff\">______<\/span>The probability of selecting an Ace is also 1\/13, so P(Ace) = 1\/13<\/p>\n<p>When we combine those two events:<\/p>\n<p><span style=\"color: #ffffff\">______<\/span>The probability of a card being a King and an Ace is 0. (It is impossible.)<\/p>\n<p><span style=\"color: #ffffff\">______<\/span>The probability of a card being a King or an Ace is (1\/13) + (1\/13) = 2\/13<\/p>\n<p>This is written like this:<\/p>\n<p><span style=\"color: #ffffff\">______<\/span>P(King and Ace) = 0<\/p>\n<p><span style=\"color: #ffffff\">______<\/span>P(King or Ace) = 1\/13 + 1\/13 = 2\/13<\/p>\n<p>Looking to get ready for the SAT? We can help with <a href=\"https:\/\/testpreparations.com\/sat-tutoring\/sat-tutoring\/\">SAT Prep<\/a><\/p>\n<p>This article was written for you by <strong>Mia<\/strong>, one of the tutors with <span class=\"tutorOrange\">Test Prep Academy.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Two events are mutually exclusive if they cannot occur simultaneously. Here are some examples of events which are mutually exclusive: Turning left and turning right are mutually exclusive because you cannot do both at the same time When you toss a coin, landing on heads or tails are mutually exclusive events When choosing a single [&hellip;]<\/p>\n","protected":false},"author":6,"featured_media":2703,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"inline_featured_image":false,"footnotes":""},"categories":[2841,3015,3021,2851],"tags":[3067,3094,3188,3364],"class_list":["post-2366","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-act","category-math-act","category-mathematics-sat","category-sat","tag-definition-of-mutually-exclusive-events","tag-finding-the-probability-of-mutually-exclusive-events","tag-introduction-to-mutually-exclusive-events","tag-what-are-mutually-exclusive-events"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/2366","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/users\/6"}],"replies":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/comments?post=2366"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/2366\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/media\/2703"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/media?parent=2366"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/categories?post=2366"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/tags?post=2366"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}