{"id":6229,"date":"2026-06-26T09:55:07","date_gmt":"2026-06-26T14:55:07","guid":{"rendered":"https:\/\/www.eastcentral.edu\/learning-center\/?page_id=6229"},"modified":"2026-06-26T09:57:51","modified_gmt":"2026-06-26T14:57:51","slug":"probability","status":"publish","type":"page","link":"https:\/\/www.eastcentral.edu\/learning-center\/probability\/","title":{"rendered":"Probability"},"content":{"rendered":"\n<h2 class=\"wp-block-heading\"><strong>General Rules<\/strong><\/h2>\n\n\n<p>\n\n\n<ul class=\"wp-block-list\">\n<li>0 \u2264 \ud835\udc43 \u2264 1\n<ul class=\"wp-block-list\">\n<li>Probabilities are values between zero and 1.<\/li>\n\n\n\n<li>They CANNOT be:\n<ul class=\"wp-block-list\">\n<li>Negative<\/li>\n\n\n\n<li>Greater than 1<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>They CAN be:\n<ul class=\"wp-block-list\">\n<li>Fractions<\/li>\n\n\n\n<li>Decimals<\/li>\n\n\n\n<li>Percentages<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>P(E) = <style>\na {\n    text-decoration: none;\n    color: #464feb;\n}\ntr th, tr td {\n    border: 1px solid #e6e6e6;\n}\ntr th {\n    background-color: #f5f5f5;\n}\n<\/style>\n<span>\\( \\frac{n(E)}{n(S)} \\)<\/span>\n<ul class=\"wp-block-list\">\n<li>To find the probability of an event (E), count the number of times the event happens and divide by the total number of outcomes in the sample space (S)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Addition Rules<\/strong><\/h2>\n\n\n<ul>\n<li>\ud835\udc43(\ud835\udc38)+\ud835\udc43(\ud835\udc38<sup>\ud835\udc50<\/sup>) =1 or 1\u2212\ud835\udc43(\ud835\udc38) =\ud835\udc43(\ud835\udc38<sup>\ud835\udc50<\/sup>)\n<ul>\n<li>The <span style=\"text-decoration: underline;\">complement<\/span> of an event is the probability that event does NOT <br \/>happen.<\/li>\n<li>Two complements add up to 100% or 1.<\/li>\n<\/ul>\n<\/li>\n<li>OR\n<ul>\n<li>Mutually Exclusive\n<ul>\n<li>Two events that do NOT happen at the same time.<\/li>\n<li>\ud835\udc43(\ud835\udc38 \ud835\udc5c\ud835\udc5f \ud835\udc39)=\ud835\udc43(\ud835\udc38)+\ud835\udc43(\ud835\udc39)<\/li>\n<\/ul>\n<\/li>\n<li>NOT Mutually Exclusive\n<ul>\n<li>Two events that DO happen at the same time.<\/li>\n<li>\ud835\udc43(\ud835\udc38 \ud835\udc5c\ud835\udc5f \ud835\udc39)=\ud835\udc43(\ud835\udc38)+\ud835\udc43(\ud835\udc39)\u2212\ud835\udc43(\ud835\udc38 \ud835\udc4e\ud835\udc5b\ud835\udc51 \ud835\udc39)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n<h2 class=\"wp-block-heading\"><strong>Multiplication Rules<\/strong><\/h2>\n\n\n<ul>\n<li>AND\n<ul>\n<li>Independent\n<ul>\n<li>Two events that are NOT affected by each other.<\/li>\n<li>\ud835\udc43(\ud835\udc38 \ud835\udc4e\ud835\udc5b\ud835\udc51 \ud835\udc39)=\ud835\udc43(\ud835\udc38)\u00d7\ud835\udc43(\ud835\udc39)<\/li>\n<\/ul>\n<\/li>\n<li>Dependent (aka NOT independent)\n<ul>\n<li>Two events that ARE affected by each other.<\/li>\n<li>\ud835\udc43(\ud835\udc38 \ud835\udc4e\ud835\udc5b\ud835\udc51 \ud835\udc39)=\ud835\udc43(\ud835\udc38)\u00d7\ud835\udc43(\ud835\udc39|\ud835\udc38)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n<li>Fundamental Counting Principle\n<ul>\n<li>If multiple independent events happen consecutively, the total number of outcomes is found by multiplying the events.\n<ul>\n<li>\ud835\udc58<sub>1<\/sub>&times;\ud835\udc58<sub>2<\/sub>&times;\ud835\udc58<sub>3<\/sub>&times;\u2026\ud835\udc58<sub>n<\/sub><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n<li>Conditional Probabilities\n<ul>\n<li>\ud835\udc43(\ud835\udc39|\ud835\udc38) = \\( \\frac{P(E \\text{ and } F)}{P(E)} \\)<\/li>\n<li>The sample space changes based on the condition that is applied.<\/li>\n<li>Key words to look out for:\n<ul>\n<li>If<\/li>\n<li>Given that<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><a href=\"https:\/\/www.eastcentral.edu\/learning-center\/wp-content\/uploads\/sites\/27\/2025\/05\/image.jpeg\"><img loading=\"lazy\" decoding=\"async\" width=\"602\" height=\"455\" src=\"https:\/\/www.eastcentral.edu\/learning-center\/wp-content\/uploads\/sites\/27\/2025\/05\/image.jpeg\" alt=\"ÌÇÐÄvlog¹ÙÍø Learning Center Logo\" class=\"wp-image-4893\" style=\"width:200px\" srcset=\"https:\/\/www.eastcentral.edu\/learning-center\/wp-content\/uploads\/sites\/27\/2025\/05\/image.jpeg 602w, https:\/\/www.eastcentral.edu\/learning-center\/wp-content\/uploads\/sites\/27\/2025\/05\/image-300x227.jpeg 300w\" sizes=\"auto, (max-width: 602px) 100vw, 602px\" \/><\/a><\/figure>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>General Rules Addition Rules \ud835\udc43(\ud835\udc38)+\ud835\udc43(\ud835\udc38\ud835\udc50) =1 or 1\u2212\ud835\udc43(\ud835\udc38) =\ud835\udc43(\ud835\udc38\ud835\udc50) The complement of an event is the probability that event does NOT happen. Two complements add up to 100% or 1. OR Mutually Exclusive Two events that do NOT happen at the same time. \ud835\udc43(\ud835\udc38 \ud835\udc5c\ud835\udc5f \ud835\udc39)=\ud835\udc43(\ud835\udc38)+\ud835\udc43(\ud835\udc39) NOT Mutually Exclusive Two events that DO happen at [&hellip;]<\/p>\n","protected":false},"author":12,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_eb_attr":"","footnotes":""},"yst_prominent_words":[],"class_list":["post-6229","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/www.eastcentral.edu\/learning-center\/wp-json\/wp\/v2\/pages\/6229","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.eastcentral.edu\/learning-center\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.eastcentral.edu\/learning-center\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.eastcentral.edu\/learning-center\/wp-json\/wp\/v2\/users\/12"}],"replies":[{"embeddable":true,"href":"https:\/\/www.eastcentral.edu\/learning-center\/wp-json\/wp\/v2\/comments?post=6229"}],"version-history":[{"count":23,"href":"https:\/\/www.eastcentral.edu\/learning-center\/wp-json\/wp\/v2\/pages\/6229\/revisions"}],"predecessor-version":[{"id":6253,"href":"https:\/\/www.eastcentral.edu\/learning-center\/wp-json\/wp\/v2\/pages\/6229\/revisions\/6253"}],"wp:attachment":[{"href":"https:\/\/www.eastcentral.edu\/learning-center\/wp-json\/wp\/v2\/media?parent=6229"}],"wp:term":[{"taxonomy":"yst_prominent_words","embeddable":true,"href":"https:\/\/www.eastcentral.edu\/learning-center\/wp-json\/wp\/v2\/yst_prominent_words?post=6229"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}