{"id":248953,"date":"2025-07-08T20:31:28","date_gmt":"2025-07-08T20:31:28","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=248953"},"modified":"2025-07-08T20:31:30","modified_gmt":"2025-07-08T20:31:30","slug":"a-test-was-given-to-a-group-of-students","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/08\/a-test-was-given-to-a-group-of-students\/","title":{"rendered":"A test was given to a group of students."},"content":{"rendered":"\n<p>A test was given to a group of students. The grades and residency are summarized below A B C Total In-State 4 9 12 25 Out-of-State 13 20 2 35 Total 17 29 14 60 If one student is chosen at random from those who took the test, find the probability that the student got a C given they are Out-of-State. Write your answer as a reduced fraction.<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-1-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>We are given the following data:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>In-State Students:<\/strong>\n<ul class=\"wp-block-list\">\n<li>Grade A: 4<\/li>\n\n\n\n<li>Grade B: 9<\/li>\n\n\n\n<li>Grade C: 12<\/li>\n\n\n\n<li>Total In-State: 25<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Out-of-State Students:<\/strong>\n<ul class=\"wp-block-list\">\n<li>Grade A: 13<\/li>\n\n\n\n<li>Grade B: 20<\/li>\n\n\n\n<li>Grade C: 2<\/li>\n\n\n\n<li>Total Out-of-State: 35<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Total:<\/strong>\n<ul class=\"wp-block-list\">\n<li>Grade A: 17<\/li>\n\n\n\n<li>Grade B: 29<\/li>\n\n\n\n<li>Grade C: 14<\/li>\n\n\n\n<li>Total Students: 60<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<p>We are asked to find the probability that a student got a C given that they are <strong>Out-of-State<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Identify the conditional probability formula<\/h3>\n\n\n\n<p>The probability of getting a C given the student is Out-of-State is a <strong>conditional probability<\/strong>. This is given by the formula:P(C\u2223Out-of-State)=Number&nbsp;of&nbsp;Out-of-State&nbsp;students&nbsp;who&nbsp;got&nbsp;a&nbsp;CTotal&nbsp;number&nbsp;of&nbsp;Out-of-State&nbsp;studentsP(\\text{C} \\mid \\text{Out-of-State}) = \\frac{\\text{Number of Out-of-State students who got a C}}{\\text{Total number of Out-of-State students}}P(C\u2223Out-of-State)=Total&nbsp;number&nbsp;of&nbsp;Out-of-State&nbsp;studentsNumber&nbsp;of&nbsp;Out-of-State&nbsp;students&nbsp;who&nbsp;got&nbsp;a&nbsp;C\u200b<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Plug in the values<\/h3>\n\n\n\n<p>From the data:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The number of <strong>Out-of-State students who got a C<\/strong> = 2<\/li>\n\n\n\n<li>The total number of <strong>Out-of-State students<\/strong> = 35<\/li>\n<\/ul>\n\n\n\n<p>Thus, the probability is:P(C\u2223Out-of-State)=235P(\\text{C} \\mid \\text{Out-of-State}) = \\frac{2}{35}P(C\u2223Out-of-State)=352\u200b<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: Simplify the fraction<\/h3>\n\n\n\n<p>The fraction 235\\frac{2}{35}352\u200b is already in its simplest form.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer:<\/h3>\n\n\n\n<p>The probability that a randomly chosen student who is <strong>Out-of-State<\/strong> got a <strong>C<\/strong> is:235\\boxed{\\frac{2}{35}}352\u200b\u200b<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation:<\/h3>\n\n\n\n<p>To find this probability, we focus on the <strong>Out-of-State<\/strong> group and then calculate how many of those students got a C. The formula for conditional probability helps us account for the total number of students in the <strong>Out-of-State<\/strong> group, which is 35. Since only 2 students in that group got a C, the probability is simply 235\\frac{2}{35}352\u200b.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner8-356.jpeg\" alt=\"\" class=\"wp-image-248954\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>A test was given to a group of students. The grades and residency are summarized below A B C Total In-State 4 9 12 25 Out-of-State 13 20 2 35 Total 17 29 14 60 If one student is chosen at random from those who took the test, find the probability that the student got [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-248953","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/248953","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=248953"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/248953\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=248953"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=248953"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=248953"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}