{"id":977,"date":"2023-06-22T01:38:42","date_gmt":"2023-06-22T01:38:42","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/probability-background-youll-need-1\/"},"modified":"2024-02-21T17:52:07","modified_gmt":"2024-02-21T17:52:07","slug":"probability-background-youll-need-1-2","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/probability-background-youll-need-1-2\/","title":{"raw":"Additional Concepts in Probability: Background You'll Need 1","rendered":"Additional Concepts in Probability: Background You&#8217;ll Need 1"},"content":{"raw":"<section class=\"textbox learningGoals\">\r\n<ul>\r\n\t<li>Identify possible outcomes of a chance experiment<\/li>\r\n<\/ul>\r\n<\/section>\r\n<h2>What is Probability?<\/h2>\r\n<p>A [pb_glossary id=\"5594\"]chance experiment[\/pb_glossary] involves making an observation in a situation where there is uncertainty about which of two or more possible <strong>outcomes<\/strong> will result.<\/p>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]831[\/ohm2_question]<\/section>\r\n<p>This list of all possible outcomes of a chance experiment is called the [pb_glossary id=\"5591\"]sample space[\/pb_glossary].<\/p>\r\n<p>In some situations, all of the possible outcomes of a chance experiment occur with the same probability. For example, when a fair six-sided die is rolled, the numbers 1, 2, 3, 4, 5, and 6 are all equally likely to occur (we say these are \u201c<strong>equally likely outcomes<\/strong>\u201d). When dealing with equally likely outcomes, it is sometimes helpful to list (or count) all of the possible outcomes.<\/p>\r\n<p>For a chance experiment, we are often interested in how likely a particular outcome (or collection of outcomes) is. An outcome or collection of outcomes for a chance experiment is called an [pb_glossary id=\"5596\"]event[\/pb_glossary].<\/p>\r\n<section class=\"textbox keyTakeaway\">\r\n<h3>probability<\/h3>\r\n<p>The <strong>probability<\/strong> of an event is a numeric measure of how likely the event is to happen.<\/p>\r\n<p>Note the conventional notation [latex]P(\\text{event})[\/latex] indicates the probability of an event.<\/p>\r\n<p>When the outcomes are equally likely, we can use the following formula to calculate the <strong>theoretical<\/strong> <strong>probability <\/strong>of event A:<\/p>\r\n<p style=\"text-align: center;\">[latex]\\text{Probability of }A = P(A) = \\dfrac{\\text{number of outcomes in event } A}{\\text{number of all possible outcomes}}[\/latex]<\/p>\r\n<\/section>\r\n<p class=\"student12ptnumberlist\" style=\"margin-left: 0in; text-indent: 0in;\">Notice that a probability can be determined by thinking of it as two counting problems followed by the computation of a related fraction.<\/p>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]835[\/ohm2_question]<\/section>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li>Identify possible outcomes of a chance experiment<\/li>\n<\/ul>\n<\/section>\n<h2>What is Probability?<\/h2>\n<p>A <a class=\"glossary-term\" aria-haspopup=\"dialog\" aria-describedby=\"definition\" href=\"#term_977_5594\">chance experiment<\/a> involves making an observation in a situation where there is uncertainty about which of two or more possible <strong>outcomes<\/strong> will result.<\/p>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm831\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=831&theme=lumen&iframe_resize_id=ohm831&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<p>This list of all possible outcomes of a chance experiment is called the <a class=\"glossary-term\" aria-haspopup=\"dialog\" aria-describedby=\"definition\" href=\"#term_977_5591\">sample space<\/a>.<\/p>\n<p>In some situations, all of the possible outcomes of a chance experiment occur with the same probability. For example, when a fair six-sided die is rolled, the numbers 1, 2, 3, 4, 5, and 6 are all equally likely to occur (we say these are \u201c<strong>equally likely outcomes<\/strong>\u201d). When dealing with equally likely outcomes, it is sometimes helpful to list (or count) all of the possible outcomes.<\/p>\n<p>For a chance experiment, we are often interested in how likely a particular outcome (or collection of outcomes) is. An outcome or collection of outcomes for a chance experiment is called an <a class=\"glossary-term\" aria-haspopup=\"dialog\" aria-describedby=\"definition\" href=\"#term_977_5596\">event<\/a>.<\/p>\n<section class=\"textbox keyTakeaway\">\n<h3>probability<\/h3>\n<p>The <strong>probability<\/strong> of an event is a numeric measure of how likely the event is to happen.<\/p>\n<p>Note the conventional notation [latex]P(\\text{event})[\/latex] indicates the probability of an event.<\/p>\n<p>When the outcomes are equally likely, we can use the following formula to calculate the <strong>theoretical<\/strong> <strong>probability <\/strong>of event A:<\/p>\n<p style=\"text-align: center;\">[latex]\\text{Probability of }A = P(A) = \\dfrac{\\text{number of outcomes in event } A}{\\text{number of all possible outcomes}}[\/latex]<\/p>\n<\/section>\n<p class=\"student12ptnumberlist\" style=\"margin-left: 0in; text-indent: 0in;\">Notice that a probability can be determined by thinking of it as two counting problems followed by the computation of a related fraction.<\/p>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm835\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=835&theme=lumen&iframe_resize_id=ohm835&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<div class=\"glossary\"><span class=\"screen-reader-text\" id=\"definition\">definition<\/span><template id=\"term_977_5594\"><div class=\"glossary__definition\" role=\"dialog\" data-id=\"term_977_5594\"><div tabindex=\"-1\"><p>making observations in situations where there is uncertainty about which of two or more possible outcomes will result<\/p>\n<\/div><button><span aria-hidden=\"true\">&times;<\/span><span class=\"screen-reader-text\">Close definition<\/span><\/button><\/div><\/template><template id=\"term_977_5591\"><div class=\"glossary__definition\" role=\"dialog\" data-id=\"term_977_5591\"><div tabindex=\"-1\"><p>the list of all possible outcomes of a chance experiment<\/p>\n<\/div><button><span aria-hidden=\"true\">&times;<\/span><span class=\"screen-reader-text\">Close definition<\/span><\/button><\/div><\/template><template id=\"term_977_5596\"><div class=\"glossary__definition\" role=\"dialog\" data-id=\"term_977_5596\"><div tabindex=\"-1\"><p>an outcome or collection of outcomes for a chance experiment<\/p>\n<\/div><button><span aria-hidden=\"true\">&times;<\/span><span class=\"screen-reader-text\">Close definition<\/span><\/button><\/div><\/template><\/div>","protected":false},"author":8,"menu_order":2,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":2910,"module-header":"background_you_need","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\/977"}],"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":11,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/977\/revisions"}],"predecessor-version":[{"id":5597,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/977\/revisions\/5597"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/parts\/2910"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/977\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=977"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=977"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=977"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=977"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}