{"id":13484,"date":"2020-12-10T08:02:24","date_gmt":"2020-12-10T02:32:24","guid":{"rendered":"https:\/\/www.aplustopper.com\/?p=13484"},"modified":"2020-12-10T11:43:44","modified_gmt":"2020-12-10T06:13:44","slug":"probability-types-events","status":"publish","type":"post","link":"https:\/\/www.aplustopper.com\/probability-types-events\/","title":{"rendered":"Probability &#8211; Types of Events"},"content":{"rendered":"<h2>Probability &#8211; Types of Events<\/h2>\n<p><iframe loading=\"lazy\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/SQLAWVkFk4E?start=87&#038;feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/p>\n<p><strong>Event:<\/strong> An event is a subset of a sample space.<\/p>\n<ol>\n<li><strong>Simple event:<\/strong> An event containing only a single sample point is called an elementary or simple event.<\/li>\n<li><strong>Compound events:<\/strong> Events obtained by combining together two or more elementary events are known as the compound events or decomposable events.<\/li>\n<li><strong>Equally likely events:<\/strong> Events are equally likely if there is no reason for an event to occur in preference to any other event.<\/li>\n<li><strong>Mutually exclusive or disjoint events:<\/strong> Events are said to be mutually exclusive or disjoint or incompatible if the occurrence of any one of them prevents the occurrence of all the others.<\/li>\n<li><strong>Mutually non-exclusive events:<\/strong> The events which are not mutually exclusive are known as compatible events or mutually non exclusive events.<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-128980\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Probability-Types-of-Events-1.jpg\" alt=\"Probability - Types of Events 1\" width=\"584\" height=\"318\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Probability-Types-of-Events-1.jpg 584w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2017\/05\/Probability-Types-of-Events-1-300x163.jpg 300w\" sizes=\"(max-width: 584px) 100vw, 584px\" \/><\/li>\n<li><strong>Independent events:<\/strong> Events are said to be independent if the happening (or non-happening) of one event is not affected by the happening (or non-happening) of others.<\/li>\n<li><strong>Dependent events:<\/strong> Two or more events are said to be dependent if the happening of one event affects (partially or totally) other event.<\/li>\n<\/ol>\n<p><iframe loading=\"lazy\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/7QlZjoLmg3I?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/p>\n<p><strong>Mutually exclusive and exhaustive system of events:<\/strong><br \/>\nLet S be the sample space associated with a random experiment. Let A<sub>1<\/sub>, A<sub>2<\/sub>, \u2026\u2026\u2026.. A<sub>n<\/sub> be subsets of S such that<br \/>\n(i) A<sub>i<\/sub> \u2229 A<sub>j<\/sub> = <em>\u03d5<\/em> for i \u2260 j and (ii) A<sub>1<\/sub> \u222a A<sub>2<\/sub> \u222a \u2026.. \u222a A<sub>n<\/sub> = S<br \/>\nThen the collection of events is said to form a mutually exclusive and exhaustive system of events.<br \/>\nIf E<sub>1<\/sub>, E<sub>2<\/sub>, \u2026\u2026\u2026.. E<sub>n<\/sub>\u00a0are elementary events associated with a random experiment, then<br \/>\n(i) E<sub>i<\/sub> \u2229 E<sub>j<\/sub> = <em>\u03d5<\/em> for i \u2260 j and (ii) E<sub>1<\/sub> \u222a E<sub>2<\/sub> \u222a \u2026.. \u222a E<sub>n<\/sub> = S<br \/>\nSo, the collection of elementary events associated with a random experiment always form a system of mutually exclusive and exhaustive system of events.<br \/>\nIn this system,\u00a0P(A<sub>1<\/sub> \u222a A<sub>2<\/sub> \u2026\u2026\u2026 \u222a A<sub>n<\/sub>) = P(A<sub>1<\/sub>) + P(A<sub>2<\/sub>) + \u2026\u2026 + P(A<sub>n<\/sub>) = 1<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Probability &#8211; Types of Events Event: An event is a subset of a sample space. Simple event: An event containing only a single sample point is called an elementary or simple event. Compound events: Events obtained by combining together two or more elementary events are known as the compound events or decomposable events. Equally likely [&hellip;]<\/p>\n","protected":false},"author":5,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_genesis_hide_title":false,"_genesis_hide_breadcrumbs":false,"_genesis_hide_singular_image":false,"_genesis_hide_footer_widgets":false,"_genesis_custom_body_class":"","_genesis_custom_post_class":"","_genesis_layout":"","footnotes":""},"categories":[5],"tags":[4971,4976,4972,4975,4977,4973,4974,4969,4970],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v17.8 (Yoast SEO v17.8) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Probability - Types of Events - A Plus Topper<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.aplustopper.com\/probability-types-events\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Probability - Types of Events\" \/>\n<meta property=\"og:description\" content=\"Probability &#8211; Types of Events Event: An event is a subset of a sample space. Simple event: An event containing only a single sample point is called an elementary or simple event. Compound events: Events obtained by combining together two or more elementary events are known as the compound events or decomposable events. 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