{"id":182715,"date":"2025-01-14T18:01:22","date_gmt":"2025-01-14T18:01:22","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=182715"},"modified":"2025-01-14T18:01:25","modified_gmt":"2025-01-14T18:01:25","slug":"in-a-survey-of-people-who-recently-bought-a-laptop","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/01\/14\/in-a-survey-of-people-who-recently-bought-a-laptop\/","title":{"rendered":"In a survey of people who recently bought a laptop"},"content":{"rendered":"\n<p>In a survey of people who recently bought a laptop, 45% ?said they were looking for a large screen, 31% ?said they were looking for a fast processor, and 58% ?said they wanted a large screen or a fast processor. If a survey respondent is selected at random, what is the probability that the respondent wanted both a large screen and a fast processor?<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\">The correct answer and explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>To solve this problem, we can use the principle of inclusion-exclusion for probabilities.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Definitions:<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>P(A)P(A): Probability of wanting a large screen = 0.450.45<\/li>\n\n\n\n<li>P(B)P(B): Probability of wanting a fast processor = 0.310.31<\/li>\n\n\n\n<li>P(A\u222aB)P(A \\cup B): Probability of wanting a large screen <strong>or<\/strong> a fast processor = 0.580.58<\/li>\n\n\n\n<li>P(A\u2229B)P(A \\cap B): Probability of wanting both a large screen <strong>and<\/strong> a fast processor (to be calculated).<\/li>\n<\/ul>\n\n\n\n<p>The formula for the union of two events is: P(A\u222aB)=P(A)+P(B)\u2212P(A\u2229B)P(A \\cup B) = P(A) + P(B) &#8211; P(A \\cap B)<\/p>\n\n\n\n<p>Rearranging to find P(A\u2229B)P(A \\cap B): P(A\u2229B)=P(A)+P(B)\u2212P(A\u222aB)P(A \\cap B) = P(A) + P(B) &#8211; P(A \\cup B)<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Calculation:<\/h3>\n\n\n\n<p>Substitute the given values: P(A\u2229B)=0.45+0.31\u22120.58P(A \\cap B) = 0.45 + 0.31 &#8211; 0.58 P(A\u2229B)=0.18P(A \\cap B) = 0.18<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer:<\/h3>\n\n\n\n<p>The probability that a respondent wanted both a large screen and a fast processor is <strong>0.18<\/strong> (or 18%).<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation:<\/h3>\n\n\n\n<p>This problem applies the principle of inclusion-exclusion to determine the overlap between two groups: people who desire a large screen and those who desire a fast processor. While P(A)P(A) and P(B)P(B) separately give the probabilities for each preference, their union P(A\u222aB)P(A \\cup B) includes all respondents who desired either one or both. However, counting P(A)+P(B)P(A) + P(B) without adjustment double-counts the individuals who fall into both categories.<\/p>\n\n\n\n<p>The subtraction of P(A\u222aB)P(A \\cup B) corrects this overcounting and isolates the shared proportion of the population that wanted both features. Hence, the result 0.180.18 reflects the probability of a respondent desiring both a large screen and a fast processor. This approach ensures that all possible outcomes are accounted for accurately and avoids double-counting overlapping preferences.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>In a survey of people who recently bought a laptop, 45% ?said they were looking for a large screen, 31% ?said they were looking for a fast processor, and 58% ?said they wanted a large screen or a fast processor. If a survey respondent is selected at random, what is the probability that the respondent [&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-182715","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/182715","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=182715"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/182715\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=182715"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=182715"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=182715"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}