{"id":3040,"date":"2023-08-30T20:26:36","date_gmt":"2023-08-30T20:26:36","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/?post_type=chapter&#038;p=3040"},"modified":"2025-05-10T22:22:23","modified_gmt":"2025-05-10T22:22:23","slug":"probability-learn-it-3-2","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/probability-learn-it-3-2\/","title":{"raw":"Probability: Learn It 3","rendered":"Probability: Learn It 3"},"content":{"raw":"<section class=\"textbox learningGoals\">\r\n<ul>\r\n\t<li>Calculate the probability of an event in a chance experiment.<\/li>\r\n\t<li>Recognize the differences between theoretical and empirical probability.<\/li>\r\n<\/ul>\r\n<\/section>\r\n<h2>Probability Values<\/h2>\r\n<section class=\"textbox recall\">The probability of an event is a numeric measure of how likely it is for the event to happen.<\/section>\r\n<p>Probability is always a value from [latex]0[\/latex] to [latex]1[\/latex], inclusive (which means that [latex]0[\/latex] and [latex]1[\/latex] are included). We can write probability as a fraction, a decimal, or a percentage from [latex]0\\%[\/latex] to [latex]100\\%[\/latex], inclusive.<\/p>\r\n<p>So, for event [latex]A[\/latex]:<\/p>\r\n<p style=\"text-align: center;\">[latex]0 \\le P(A) \\le 1[\/latex]<\/p>\r\n<p style=\"text-align: center;\">or<\/p>\r\n<p style=\"text-align: center;\">[latex]0\\% \\le P(A) \\le 100\\%[\/latex]<\/p>\r\n<p>In the world of probabilities, numbers between [latex]0[\/latex] and [latex]1[\/latex] hold special significance. These numbers represent the likelihood or chance of an event occurring. It allows us to express how likely or unlikely an event is, offering a clear and intuitive framework for reasoning about uncertainty and making informed decisions based on the likelihood of various outcomes.<\/p>\r\n<section class=\"textbox proTip\">Probability values range from 0 to 1, representing the likelihood of an event happening. Here's how you can categorize these values:\r\n\r\n<table>\r\n<tbody>\r\n<tr>\r\n<th>Probability Range<\/th>\r\n<td>0<\/td>\r\n<td>(0, 0.5)<\/td>\r\n<td>(0.5, 1)<\/td>\r\n<td>1<\/td>\r\n<\/tr>\r\n<tr>\r\n<th>Event Likelihood<\/th>\r\n<td>Impossible<\/td>\r\n<td>Improbable<\/td>\r\n<td>Probable<\/td>\r\n<td>Certain<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<ol>\r\n\t<li><strong>Impossible Event<\/strong>: This is when the probability of an event is 0. It means that there is no chance that the event will happen.<\/li>\r\n\t<li>\r\n<p><strong>Improbable Event<\/strong>: This is when the probability of an event is greater than 0 but less than 0.5. These events are not expected to happen often, but they are not impossible.<\/p>\r\n<\/li>\r\n\t<li>\r\n<p><strong>Probable Event<\/strong>: This is when the probability of an event is greater than 0.5 but less than 1. These events are more likely to happen than not.<\/p>\r\n<\/li>\r\n\t<li>\r\n<p><strong>Certain Event<\/strong>: This is when the probability of an event is 1. This means that the event is guaranteed to happen.<\/p>\r\n<\/li>\r\n<\/ol>\r\n<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]1001[\/ohm2_question]<\/section>\r\n<section>\r\n<section class=\"textbox example\">Calculate the following probabilities from flipping a fair coin (assuming that it cannot land on an edge)\r\n\r\n<ol>\r\n\t<li>Find [latex]P(\\text{either getting a head or a tail})[\/latex].<br \/>\r\n[reveal-answer q=\"202010\"]Show solution[\/reveal-answer]<br \/>\r\n[hidden-answer a=\"202010\"]The probability that you either get a head or a tail after flipping a fair coin is equal to [latex]1[\/latex] because it is certain that you will get either a head or a tail. Thus, [latex]P(\\text{either getting a head or a tail}) = 1.[\/latex]<br \/>\r\nAlso, note that getting either a head or a tail comprised the whole sample space.<br \/>\r\nThe sample space is [latex]S=\\{H, T\\}[\/latex].<br \/>\r\nTherefore, [latex]P(S) = 1[\/latex].[\/hidden-answer]<\/li>\r\n\t<li>\u00a0Find [latex]P(\\text{land on an edge})[\/latex]. [reveal-answer q=\"14413\"]Show solution[\/reveal-answer][hidden-answer a=\"14413\"]The prompt states that it cannot land on an edge.<br \/>\r\nThus, [latex]P(\\text{land on an edge}) = 0.[\/latex][\/hidden-answer]<\/li>\r\n<\/ol>\r\n<\/section>\r\n<\/section>\r\n<section>\r\n<section class=\"textbox proTip\">\r\n<ul>\r\n\t<li>To put it simply, if an event is impossible, its probability is [latex]0[\/latex].<\/li>\r\n\t<li>Conversely, if an event is certain to happen, its probability is [latex]1[\/latex].<\/li>\r\n<\/ul>\r\n<\/section>\r\n<\/section>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li>Calculate the probability of an event in a chance experiment.<\/li>\n<li>Recognize the differences between theoretical and empirical probability.<\/li>\n<\/ul>\n<\/section>\n<h2>Probability Values<\/h2>\n<section class=\"textbox recall\">The probability of an event is a numeric measure of how likely it is for the event to happen.<\/section>\n<p>Probability is always a value from [latex]0[\/latex] to [latex]1[\/latex], inclusive (which means that [latex]0[\/latex] and [latex]1[\/latex] are included). We can write probability as a fraction, a decimal, or a percentage from [latex]0\\%[\/latex] to [latex]100\\%[\/latex], inclusive.<\/p>\n<p>So, for event [latex]A[\/latex]:<\/p>\n<p style=\"text-align: center;\">[latex]0 \\le P(A) \\le 1[\/latex]<\/p>\n<p style=\"text-align: center;\">or<\/p>\n<p style=\"text-align: center;\">[latex]0\\% \\le P(A) \\le 100\\%[\/latex]<\/p>\n<p>In the world of probabilities, numbers between [latex]0[\/latex] and [latex]1[\/latex] hold special significance. These numbers represent the likelihood or chance of an event occurring. It allows us to express how likely or unlikely an event is, offering a clear and intuitive framework for reasoning about uncertainty and making informed decisions based on the likelihood of various outcomes.<\/p>\n<section class=\"textbox proTip\">Probability values range from 0 to 1, representing the likelihood of an event happening. Here&#8217;s how you can categorize these values:<\/p>\n<table>\n<tbody>\n<tr>\n<th>Probability Range<\/th>\n<td>0<\/td>\n<td>(0, 0.5)<\/td>\n<td>(0.5, 1)<\/td>\n<td>1<\/td>\n<\/tr>\n<tr>\n<th>Event Likelihood<\/th>\n<td>Impossible<\/td>\n<td>Improbable<\/td>\n<td>Probable<\/td>\n<td>Certain<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<ol>\n<li><strong>Impossible Event<\/strong>: This is when the probability of an event is 0. It means that there is no chance that the event will happen.<\/li>\n<li>\n<p><strong>Improbable Event<\/strong>: This is when the probability of an event is greater than 0 but less than 0.5. These events are not expected to happen often, but they are not impossible.<\/p>\n<\/li>\n<li>\n<p><strong>Probable Event<\/strong>: This is when the probability of an event is greater than 0.5 but less than 1. These events are more likely to happen than not.<\/p>\n<\/li>\n<li>\n<p><strong>Certain Event<\/strong>: This is when the probability of an event is 1. This means that the event is guaranteed to happen.<\/p>\n<\/li>\n<\/ol>\n<\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm1001\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=1001&theme=lumen&iframe_resize_id=ohm1001&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section>\n<section class=\"textbox example\">Calculate the following probabilities from flipping a fair coin (assuming that it cannot land on an edge)<\/p>\n<ol>\n<li>Find [latex]P(\\text{either getting a head or a tail})[\/latex].\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q202010\">Show solution<\/button><\/p>\n<div id=\"q202010\" class=\"hidden-answer\" style=\"display: none\">The probability that you either get a head or a tail after flipping a fair coin is equal to [latex]1[\/latex] because it is certain that you will get either a head or a tail. Thus, [latex]P(\\text{either getting a head or a tail}) = 1.[\/latex]<br \/>\nAlso, note that getting either a head or a tail comprised the whole sample space.<br \/>\nThe sample space is [latex]S=\\{H, T\\}[\/latex].<br \/>\nTherefore, [latex]P(S) = 1[\/latex].<\/div>\n<\/div>\n<\/li>\n<li>\u00a0Find [latex]P(\\text{land on an edge})[\/latex].\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q14413\">Show solution<\/button><\/p>\n<div id=\"q14413\" class=\"hidden-answer\" style=\"display: none\">The prompt states that it cannot land on an edge.<br \/>\nThus, [latex]P(\\text{land on an edge}) = 0.[\/latex]<\/div>\n<\/div>\n<\/li>\n<\/ol>\n<\/section>\n<\/section>\n<section>\n<section class=\"textbox proTip\">\n<ul>\n<li>To put it simply, if an event is impossible, its probability is [latex]0[\/latex].<\/li>\n<li>Conversely, if an event is certain to happen, its probability is [latex]1[\/latex].<\/li>\n<\/ul>\n<\/section>\n<\/section>\n","protected":false},"author":12,"menu_order":6,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":974,"module-header":"learn_it","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\/3040"}],"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\/12"}],"version-history":[{"count":18,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/3040\/revisions"}],"predecessor-version":[{"id":6528,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/3040\/revisions\/6528"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/parts\/974"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/3040\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=3040"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=3040"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=3040"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=3040"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}