{"id":1019,"date":"2023-06-22T01:45:06","date_gmt":"2023-06-22T01:45:06","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/probability-distributions-learn-it-3\/"},"modified":"2025-05-16T02:20:08","modified_gmt":"2025-05-16T02:20:08","slug":"probability-distributions-learn-it-3","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/probability-distributions-learn-it-3\/","title":{"raw":"Probability Distributions: Learn It 3","rendered":"Probability Distributions: Learn It 3"},"content":{"raw":"<section class=\"textbox learningGoals\">\r\n<ul>\r\n\t<li>Understand the concept of a probability distribution and its role in describing the behavior of a random variable.<\/li>\r\n\t<li>Describe the characteristics of probability distributions.<\/li>\r\n<\/ul>\r\n<\/section>\r\n<section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]1432[\/ohm2_question]<\/section>\r\n<p>Sometimes we carry out a chance experiment multiple times and count the number of \u201csuccesses.\u201d To describe this scenario, we could use a <strong>probability distribution,<\/strong>\u00a0which lists all possible values of a random variable and the probabilities associated with those values.<\/p>\r\n<section class=\"textbox example\">Suppose we flip a coin twice. The following is a complete list of possible values:\r\n\r\n<ul>\r\n\t<li>Heads on the first flip and heads on the second flip<\/li>\r\n\t<li>Heads on the first flip and tails on the second flip<\/li>\r\n\t<li>Tails on the first flip and heads on the second flip<\/li>\r\n\t<li>Tails on the first flip and tails on the second flip<\/li>\r\n<\/ul>\r\n<p>You may have to define \"success\" in different scenarios. For example, you may define \"success\" and create the probability distribution for the number of heads or tails that would occur in [latex]2[\/latex] coin flips.<\/p>\r\n<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]1434[\/ohm2_question]<\/section>\r\n<section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]12060[\/ohm2_question]<\/section>\r\n<\/section>\r\n<\/section>\r\n<section class=\"textbox example\">[reveal-answer q=\"445561\"]See the example question[\/reveal-answer]<br \/>\r\n[hidden-answer a=\"445561\"][ohm2_question hide_question_numbers=1]1187[\/ohm2_question][\/hidden-answer]<br \/>\r\n[videopicker divId=\"tnh-video-picker\" title=\"Analyze Probability Distributions in Graphs and Tables\" label=\"Select Instructor\"]<br \/>\r\n[videooption displayName=\"Dr. Pamela E. Harris\" value=\"https:\/\/www.youtube.com\/watch?v=YOpKdjwFt0g\"][videooption displayName=\"Dr. Aris Winger\" value=\"https:\/\/www.youtube.com\/watch?v=2R80C8ScPC0\"] [videooption displayName=\"Dr. Lane Fisher\" value=\"https:\/\/www.youtube.com\/watch?v=cYK-pWNMHw4\"]<br \/>\r\n[\/videopicker]<\/section>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li>Understand the concept of a probability distribution and its role in describing the behavior of a random variable.<\/li>\n<li>Describe the characteristics of probability distributions.<\/li>\n<\/ul>\n<\/section>\n<section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm1432\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=1432&theme=lumen&iframe_resize_id=ohm1432&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<p>Sometimes we carry out a chance experiment multiple times and count the number of \u201csuccesses.\u201d To describe this scenario, we could use a <strong>probability distribution,<\/strong>\u00a0which lists all possible values of a random variable and the probabilities associated with those values.<\/p>\n<section class=\"textbox example\">Suppose we flip a coin twice. The following is a complete list of possible values:<\/p>\n<ul>\n<li>Heads on the first flip and heads on the second flip<\/li>\n<li>Heads on the first flip and tails on the second flip<\/li>\n<li>Tails on the first flip and heads on the second flip<\/li>\n<li>Tails on the first flip and tails on the second flip<\/li>\n<\/ul>\n<p>You may have to define &#8220;success&#8221; in different scenarios. For example, you may define &#8220;success&#8221; and create the probability distribution for the number of heads or tails that would occur in [latex]2[\/latex] coin flips.<\/p>\n<\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm1434\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=1434&theme=lumen&iframe_resize_id=ohm1434&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm12060\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=12060&theme=lumen&iframe_resize_id=ohm12060&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<\/section>\n<\/section>\n<section class=\"textbox example\">\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q445561\">See the example question<\/button><\/p>\n<div id=\"q445561\" class=\"hidden-answer\" style=\"display: none\"><iframe loading=\"lazy\" id=\"ohm1187\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=1187&theme=lumen&iframe_resize_id=ohm1187&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/div>\n<\/div>\n<div class=\"wp-nocaption \"><\/div>\n<div id=\"tnh-video-picker\" class=\"videoPicker\">\n<h3>Analyze Probability Distributions in Graphs and Tables<\/h3>\n<form><label>Select Instructor:<\/label><select name=\"video\"><option value=\"https:\/\/www.youtube.com\/embed\/YOpKdjwFt0g\">Dr. Pamela E. Harris<\/option><option value=\"https:\/\/www.youtube.com\/embed\/2R80C8ScPC0\">Dr. Aris Winger<\/option><option value=\"https:\/\/www.youtube.com\/embed\/cYK-pWNMHw4\">Dr. Lane Fisher<\/option><\/select><\/form>\n<div class=\"videoContainer\"><iframe src=\"https:\/\/www.youtube.com\/embed\/YOpKdjwFt0g\" allowfullscreen><\/iframe><\/div>\n<\/section>\n","protected":false},"author":8,"menu_order":7,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":3053,"module-header":"learn_it","content_attributions":[],"internal_book_links":[],"video_content":[{"divId":"tnh-video-picker","title":"Analyze Probability Distributions in Graphs and Tables","label":"Select Instructor","video_collection":[{"displayName":"Dr. Pamela E. 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