{"id":4042,"date":"2020-04-05T01:44:07","date_gmt":"2020-04-05T01:44:07","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/mathforlibscoreq\/?post_type=chapter&#038;p=4042"},"modified":"2021-02-06T00:03:09","modified_gmt":"2021-02-06T00:03:09","slug":"finding-the-probability-of-an-event","status":"web-only","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/chapter\/finding-the-probability-of-an-event\/","title":{"raw":"Finding the Probability of an Event","rendered":"Finding the Probability of an Event"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Find the probability of an event given the number of favorable outcomes and the total number of outcomes possible<\/li>\r\n<\/ul>\r\n<\/div>\r\n<p>The probability of an event tells us how likely that event is to occur. We usually write probabilities as fractions or decimals.\r\nFor example, picture a fruit bowl that contains five pieces of fruit - three bananas and two apples.<\/p>\r\n<p>If you want to choose one piece of fruit to eat for a snack and don\u2019t care what it is, there is a [latex]{\\Large\\frac{3}{5}}[\/latex] probability you will choose a banana, because there are three bananas out of the total of five pieces of fruit. The probability of an event is the number of favorable outcomes divided by the total number of outcomes.<\/p>\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221824\/CNX_BMath_Figure_05_05_007_img.png\" alt=\"Two equations are shown. The top equation says the probability of an event equals the number of favorable outcomes over the total number of outcomes. The bottom equation says the probability of choosing a banana equals 3 over 5. There is a blue arrow pointing to the 3 with the text, 'There are 3 bananas.' There is a blue arrow pointing to the 5 with the text, 'There are 5 pieces of fruit.'\" \/>\r\n<div class=\"textbox shaded\">\r\n<h3>Probability<\/h3>\r\nThe probability of an event is the number of favorable outcomes divided by the total number of outcomes possible.\r\n\r\n[latex]\\text{Probability}={\\Large\\frac{\\text{number of favorable outcomes}}{\\text{total number of outcomes}}}[\/latex]\r\n\r\nConverting the fraction [latex]{\\Large\\frac{3}{5}}[\/latex] to a decimal, we would say there is a [latex]0.6[\/latex] probability of choosing a banana.\r\n\r\n[latex]\\begin{array}{}\\\\ \\text{Probability of choosing a banana}={\\Large\\frac{3}{5}}\\hfill \\\\ \\text{Probability of choosing a banana}=0.6\\hfill \\end{array}[\/latex]\r\n\r\n<\/div>\r\nThis basic definition of probability assumes that all the outcomes are equally likely to occur. If you study probabilities in a later math class, you\u2019ll learn about several other ways to calculate probabilities.\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nThe ski club is holding a raffle to raise money. They sold [latex]100[\/latex] tickets. All of the tickets are placed in a jar. One ticket will be pulled out of the jar at random, and the winner will receive a prize. Cherie bought one raffle ticket.\r\n1. Find the probability she will win the prize.\r\n2. Convert the fraction to a decimal.\r\n\r\nSolution\r\n<table id=\"eip-id1168467196431\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>1.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>What are you asked to find?<\/td>\r\n<td>The probability Cherie wins the prize.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>What is the number of favorable outcomes?<\/td>\r\n<td>[latex]1[\/latex], because Cherie has [latex]1[\/latex] ticket.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Use the definition of probability.<\/td>\r\n<td>[latex]\\text{Probability of an event}={\\Large\\frac{\\text{number of favorable outcomes}}{\\text{total number of outcomes}}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Substitute into the numerator and denominator.<\/td>\r\n<td>[latex]\\text{Probability Cherie wins}={\\Large\\frac{1}{100}}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table id=\"eip-id1168468509885\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>2.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Convert the fraction to a decimal.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write the probability as a fraction.<\/td>\r\n<td>[latex]\\text{Probability}={\\Large\\frac{1}{100}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Convert the fraction to a decimal.<\/td>\r\n<td>[latex]\\text{Probability}=0.01[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]146446[\/ohm_question]\r\n\r\n[ohm_question]146447[\/ohm_question]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nThree women and five men interviewed for a job. One of the candidates will be offered the job.\r\n1. Find the probability the job is offered to a woman.\r\n2. Convert the fraction to a decimal.\r\n[reveal-answer q=\"624032\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"624032\"]\r\n\r\nSolution\r\n<table id=\"eip-id1168467113660\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>1.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>What are you asked to find?<\/td>\r\n<td>The probability the job is offered to a woman.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>What is the number of favorable outcomes?<\/td>\r\n<td>[latex]3[\/latex], because there are three women.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>What are the total number of outcomes?<\/td>\r\n<td>[latex]8[\/latex], because [latex]8[\/latex] people interviewed.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Use the definition of probability.<\/td>\r\n<td>[latex]\\text{Probability of an event}={\\Large\\frac{\\text{number of favorable outcomes}}{\\text{total number of outcomes}}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Substitute into the numerator and denominator.<\/td>\r\n<td>[latex]\\text{Probability}={\\Large\\frac{3}{8}}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table id=\"eip-id1168468597704\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>2.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Convert the fraction to a decimal.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write the probability as a fraction.<\/td>\r\n<td>[latex]\\text{Probability}={\\Large\\frac{3}{8}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Convert the fraction to a decimal.<\/td>\r\n<td>[latex]\\text{Probability}=0.375[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>TRY\u00a0IT<\/h3>\r\n[ohm_question]146451[\/ohm_question]\r\n\r\n[ohm_question]146452[\/ohm_question]\r\n\r\n<\/div>\r\nThe following video contains another example of how to compute the probability of an event and write it as either a fraction or decimal.\r\n\r\nhttps:\/\/youtu.be\/eqpuG2uQDI0","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Find the probability of an event given the number of favorable outcomes and the total number of outcomes possible<\/li>\n<\/ul>\n<\/div>\n<p>The probability of an event tells us how likely that event is to occur. We usually write probabilities as fractions or decimals.<br \/>\nFor example, picture a fruit bowl that contains five pieces of fruit &#8211; three bananas and two apples.<\/p>\n<p>If you want to choose one piece of fruit to eat for a snack and don\u2019t care what it is, there is a [latex]{\\Large\\frac{3}{5}}[\/latex] probability you will choose a banana, because there are three bananas out of the total of five pieces of fruit. The probability of an event is the number of favorable outcomes divided by the total number of outcomes.<\/p>\n<p><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221824\/CNX_BMath_Figure_05_05_007_img.png\" alt=\"Two equations are shown. The top equation says the probability of an event equals the number of favorable outcomes over the total number of outcomes. The bottom equation says the probability of choosing a banana equals 3 over 5. There is a blue arrow pointing to the 3 with the text, 'There are 3 bananas.' There is a blue arrow pointing to the 5 with the text, 'There are 5 pieces of fruit.'\" \/><\/p>\n<div class=\"textbox shaded\">\n<h3>Probability<\/h3>\n<p>The probability of an event is the number of favorable outcomes divided by the total number of outcomes possible.<\/p>\n<p>[latex]\\text{Probability}={\\Large\\frac{\\text{number of favorable outcomes}}{\\text{total number of outcomes}}}[\/latex]<\/p>\n<p>Converting the fraction [latex]{\\Large\\frac{3}{5}}[\/latex] to a decimal, we would say there is a [latex]0.6[\/latex] probability of choosing a banana.<\/p>\n<p>[latex]\\begin{array}{}\\\\ \\text{Probability of choosing a banana}={\\Large\\frac{3}{5}}\\hfill \\\\ \\text{Probability of choosing a banana}=0.6\\hfill \\end{array}[\/latex]<\/p>\n<\/div>\n<p>This basic definition of probability assumes that all the outcomes are equally likely to occur. If you study probabilities in a later math class, you\u2019ll learn about several other ways to calculate probabilities.<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>The ski club is holding a raffle to raise money. They sold [latex]100[\/latex] tickets. All of the tickets are placed in a jar. One ticket will be pulled out of the jar at random, and the winner will receive a prize. Cherie bought one raffle ticket.<br \/>\n1. Find the probability she will win the prize.<br \/>\n2. Convert the fraction to a decimal.<\/p>\n<p>Solution<\/p>\n<table id=\"eip-id1168467196431\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>1.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>What are you asked to find?<\/td>\n<td>The probability Cherie wins the prize.<\/td>\n<\/tr>\n<tr>\n<td>What is the number of favorable outcomes?<\/td>\n<td>[latex]1[\/latex], because Cherie has [latex]1[\/latex] ticket.<\/td>\n<\/tr>\n<tr>\n<td>Use the definition of probability.<\/td>\n<td>[latex]\\text{Probability of an event}={\\Large\\frac{\\text{number of favorable outcomes}}{\\text{total number of outcomes}}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Substitute into the numerator and denominator.<\/td>\n<td>[latex]\\text{Probability Cherie wins}={\\Large\\frac{1}{100}}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1168468509885\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>2.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Convert the fraction to a decimal.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Write the probability as a fraction.<\/td>\n<td>[latex]\\text{Probability}={\\Large\\frac{1}{100}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Convert the fraction to a decimal.<\/td>\n<td>[latex]\\text{Probability}=0.01[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146446\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146446&theme=oea&iframe_resize_id=ohm146446&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<p><iframe loading=\"lazy\" id=\"ohm146447\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146447&theme=oea&iframe_resize_id=ohm146447&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Three women and five men interviewed for a job. One of the candidates will be offered the job.<br \/>\n1. Find the probability the job is offered to a woman.<br \/>\n2. Convert the fraction to a decimal.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q624032\">Show Solution<\/span><\/p>\n<div id=\"q624032\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<\/p>\n<table id=\"eip-id1168467113660\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>1.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>What are you asked to find?<\/td>\n<td>The probability the job is offered to a woman.<\/td>\n<\/tr>\n<tr>\n<td>What is the number of favorable outcomes?<\/td>\n<td>[latex]3[\/latex], because there are three women.<\/td>\n<\/tr>\n<tr>\n<td>What are the total number of outcomes?<\/td>\n<td>[latex]8[\/latex], because [latex]8[\/latex] people interviewed.<\/td>\n<\/tr>\n<tr>\n<td>Use the definition of probability.<\/td>\n<td>[latex]\\text{Probability of an event}={\\Large\\frac{\\text{number of favorable outcomes}}{\\text{total number of outcomes}}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Substitute into the numerator and denominator.<\/td>\n<td>[latex]\\text{Probability}={\\Large\\frac{3}{8}}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1168468597704\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>2.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Convert the fraction to a decimal.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Write the probability as a fraction.<\/td>\n<td>[latex]\\text{Probability}={\\Large\\frac{3}{8}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Convert the fraction to a decimal.<\/td>\n<td>[latex]\\text{Probability}=0.375[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>TRY\u00a0IT<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146451\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146451&theme=oea&iframe_resize_id=ohm146451&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<p><iframe loading=\"lazy\" id=\"ohm146452\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146452&theme=oea&iframe_resize_id=ohm146452&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>The following video contains another example of how to compute the probability of an event and write it as either a fraction or decimal.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"(New Version Available) Ex:  Basic Example of Finding Probability - Running a Red Light\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/eqpuG2uQDI0?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-4042\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Original<\/div><ul class=\"citation-list\"><li>Question ID 146452, 146451, 146447, 146446. <strong>Authored by<\/strong>: Lumen Learning. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>Revision and Adaptation. <strong>Provided by<\/strong>: Lumen Learning. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Ex: Basic Example of Finding Probability - Running a Red Light. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/eqpuG2uQDI0\">https:\/\/youtu.be\/eqpuG2uQDI0<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Specific attribution<\/div><ul class=\"citation-list\"><li>Prealgebra. <strong>Provided by<\/strong>: OpenStax. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: Download for free at http:\/\/cnx.org\/contents\/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757<\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":25777,"menu_order":8,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc-attribution\",\"description\":\"Prealgebra\",\"author\":\"\",\"organization\":\"OpenStax\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Download for free at http:\/\/cnx.org\/contents\/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757\"},{\"type\":\"cc\",\"description\":\"Ex: Basic Example of Finding Probability - Running a Red Light\",\"author\":\"James Sousa (Mathispower4u.com)\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/eqpuG2uQDI0\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"original\",\"description\":\"Question ID 146452, 146451, 146447, 146446\",\"author\":\"Lumen Learning\",\"organization\":\"\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"original\",\"description\":\"Revision and Adaptation\",\"author\":\"\",\"organization\":\"Lumen Learning\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-4042","chapter","type-chapter","status-web-only","hentry"],"part":329,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/4042","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/users\/25777"}],"version-history":[{"count":1,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/4042\/revisions"}],"predecessor-version":[{"id":4043,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/4042\/revisions\/4043"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/parts\/329"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/4042\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/media?parent=4042"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapter-type?post=4042"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/contributor?post=4042"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/license?post=4042"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}