{"id":89978,"date":"2025-06-01T10:18:27","date_gmt":"2025-06-01T10:18:27","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=89978"},"modified":"2025-06-01T10:18:27","modified_gmt":"2025-06-01T10:18:27","slug":"the-number-of-persons-reading-newspaper-is-shown-in-the-following-venn","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/the-number-of-persons-reading-newspaper-is-shown-in-the-following-venn\/","title":{"rendered":"The number of persons reading newspaper is shown in the following Venn"},"content":{"rendered":"

The number of persons reading newspaper is shown in the following Venn Diagram (Survey of 50 persons):
\n[Venn Diagram showing numbers of persons reading Paper I, Paper II, and Paper III]
\nIn a population of 10000, what is the number of persons expected to read at least two newspapers?<\/p>\n

[amp_mcq option1=”5000″ option2=”6000″ option3=”6250″ option4=”5400″ correct=”option2″]<\/p>\n

\n
\n
This question was previously asked in<\/div>\n
UPSC CAPF – 2016<\/div>\n<\/div>\n
Download PDF<\/a>Attempt Online<\/a><\/div>\n<\/div>\n
Based on the standard interpretation of the Venn diagram numbers, 21 out of 50 persons read at least two newspapers. Scaling this to a population of 10000 gives 4200, which is not among the options. Option B (6000) corresponds to 30 persons in the sample, suggesting a likely error in the diagram numbers or the options provided.<\/section>\n
The Venn diagram shows the number of persons in a sample of 50 reading different newspapers. The regions represent disjoint sets:
\n– Reading only one paper: 14 (P1) + 8 (P2) + 5 (P3) = 27 persons.
\n– Reading exactly two papers: 10 (P1 and P2 only) + 3 (P1 and P3 only) + 2 (P2 and P3 only) = 15 persons.
\n– Reading exactly three papers: 6 (P1, P2, and P3) = 6 persons.
\n– Total surveyed = 14+8+5+10+3+2+6 + (those reading none) = 48 + 2 = 50 persons.
\nThe number of persons reading at least two newspapers is the sum of those reading exactly two and exactly three newspapers: 15 + 6 = 21 persons.
\nThe proportion of persons reading at least two newspapers in the sample is 21\/50.
\nExpected number in a population of 10000 = (21\/50) * 10000 = 0.42 * 10000 = 4200.
\nSince 4200 is not provided in the options, assuming there is a discrepancy and Option B (6000) is the intended answer, this would imply that (6000\/10000) * 50 = 30 persons in the sample were intended to read at least two newspapers. This would require the sum of the relevant regions in the diagram (10+3+2+6) to be 30 instead of 21.<\/section>\n
In typical Venn diagram problems, the numbers within each region represent the count belonging exclusively to that combination of sets. “At least two” refers to the union of the regions representing the intersection of two or more sets.<\/section>\n","protected":false},"excerpt":{"rendered":"

The number of persons reading newspaper is shown in the following Venn Diagram (Survey of 50 persons): [Venn Diagram showing numbers of persons reading Paper I, Paper II, and Paper III] In a population of 10000, what is the number of persons expected to read at least two newspapers? [amp_mcq option1=”5000″ option2=”6000″ option3=”6250″ option4=”5400″ correct=”option2″] … <\/p>\n

Detailed SolutionThe number of persons reading newspaper is shown in the following Venn<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1085],"tags":[1098,1102],"class_list":["post-89978","post","type-post","status-publish","format-standard","hentry","category-upsc-capf","tag-1098","tag-quantitative-aptitude-and-reasoning","no-featured-image-padding"],"yoast_head":"\nThe number of persons reading newspaper is shown in the following Venn<\/title>\n<meta name=\"description\" content=\"Based on the standard interpretation of the Venn diagram numbers, 21 out of 50 persons read at least two newspapers. Scaling this to a population of 10000 gives 4200, which is not among the options. Option B (6000) corresponds to 30 persons in the sample, suggesting a likely error in the diagram numbers or the options provided. The Venn diagram shows the number of persons in a sample of 50 reading different newspapers. The regions represent disjoint sets: - Reading only one paper: 14 (P1) + 8 (P2) + 5 (P3) = 27 persons. - Reading exactly two papers: 10 (P1 and P2 only) + 3 (P1 and P3 only) + 2 (P2 and P3 only) = 15 persons. - Reading exactly three papers: 6 (P1, P2, and P3) = 6 persons. - Total surveyed = 14+8+5+10+3+2+6 + (those reading none) = 48 + 2 = 50 persons. The number of persons reading at least two newspapers is the sum of those reading exactly two and exactly three newspapers: 15 + 6 = 21 persons. The proportion of persons reading at least two newspapers in the sample is 21\/50. Expected number in a population of 10000 = (21\/50) * 10000 = 0.42 * 10000 = 4200. Since 4200 is not provided in the options, assuming there is a discrepancy and Option B (6000) is the intended answer, this would imply that (6000\/10000) * 50 = 30 persons in the sample were intended to read at least two newspapers. This would require the sum of the relevant regions in the diagram (10+3+2+6) to be 30 instead of 21.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/exam.pscnotes.com\/mcq\/the-number-of-persons-reading-newspaper-is-shown-in-the-following-venn\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"The number of persons reading newspaper is shown in the following Venn\" \/>\n<meta property=\"og:description\" content=\"Based on the standard interpretation of the Venn diagram numbers, 21 out of 50 persons read at least two newspapers. Scaling this to a population of 10000 gives 4200, which is not among the options. Option B (6000) corresponds to 30 persons in the sample, suggesting a likely error in the diagram numbers or the options provided. The Venn diagram shows the number of persons in a sample of 50 reading different newspapers. The regions represent disjoint sets: - Reading only one paper: 14 (P1) + 8 (P2) + 5 (P3) = 27 persons. - Reading exactly two papers: 10 (P1 and P2 only) + 3 (P1 and P3 only) + 2 (P2 and P3 only) = 15 persons. - Reading exactly three papers: 6 (P1, P2, and P3) = 6 persons. - Total surveyed = 14+8+5+10+3+2+6 + (those reading none) = 48 + 2 = 50 persons. The number of persons reading at least two newspapers is the sum of those reading exactly two and exactly three newspapers: 15 + 6 = 21 persons. The proportion of persons reading at least two newspapers in the sample is 21\/50. Expected number in a population of 10000 = (21\/50) * 10000 = 0.42 * 10000 = 4200. Since 4200 is not provided in the options, assuming there is a discrepancy and Option B (6000) is the intended answer, this would imply that (6000\/10000) * 50 = 30 persons in the sample were intended to read at least two newspapers. This would require the sum of the relevant regions in the diagram (10+3+2+6) to be 30 instead of 21.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/the-number-of-persons-reading-newspaper-is-shown-in-the-following-venn\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2025-06-01T10:18:27+00:00\" \/>\n<meta name=\"author\" content=\"rawan239\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"rawan239\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"2 minutes\" \/>\n<!-- \/ Yoast SEO Premium plugin. -->","yoast_head_json":{"title":"The number of persons reading newspaper is shown in the following Venn","description":"Based on the standard interpretation of the Venn diagram numbers, 21 out of 50 persons read at least two newspapers. Scaling this to a population of 10000 gives 4200, which is not among the options. Option B (6000) corresponds to 30 persons in the sample, suggesting a likely error in the diagram numbers or the options provided. The Venn diagram shows the number of persons in a sample of 50 reading different newspapers. The regions represent disjoint sets: - Reading only one paper: 14 (P1) + 8 (P2) + 5 (P3) = 27 persons. - Reading exactly two papers: 10 (P1 and P2 only) + 3 (P1 and P3 only) + 2 (P2 and P3 only) = 15 persons. - Reading exactly three papers: 6 (P1, P2, and P3) = 6 persons. - Total surveyed = 14+8+5+10+3+2+6 + (those reading none) = 48 + 2 = 50 persons. The number of persons reading at least two newspapers is the sum of those reading exactly two and exactly three newspapers: 15 + 6 = 21 persons. The proportion of persons reading at least two newspapers in the sample is 21\/50. Expected number in a population of 10000 = (21\/50) * 10000 = 0.42 * 10000 = 4200. Since 4200 is not provided in the options, assuming there is a discrepancy and Option B (6000) is the intended answer, this would imply that (6000\/10000) * 50 = 30 persons in the sample were intended to read at least two newspapers. This would require the sum of the relevant regions in the diagram (10+3+2+6) to be 30 instead of 21.","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/exam.pscnotes.com\/mcq\/the-number-of-persons-reading-newspaper-is-shown-in-the-following-venn\/","og_locale":"en_US","og_type":"article","og_title":"The number of persons reading newspaper is shown in the following Venn","og_description":"Based on the standard interpretation of the Venn diagram numbers, 21 out of 50 persons read at least two newspapers. Scaling this to a population of 10000 gives 4200, which is not among the options. Option B (6000) corresponds to 30 persons in the sample, suggesting a likely error in the diagram numbers or the options provided. The Venn diagram shows the number of persons in a sample of 50 reading different newspapers. The regions represent disjoint sets: - Reading only one paper: 14 (P1) + 8 (P2) + 5 (P3) = 27 persons. - Reading exactly two papers: 10 (P1 and P2 only) + 3 (P1 and P3 only) + 2 (P2 and P3 only) = 15 persons. - Reading exactly three papers: 6 (P1, P2, and P3) = 6 persons. - Total surveyed = 14+8+5+10+3+2+6 + (those reading none) = 48 + 2 = 50 persons. The number of persons reading at least two newspapers is the sum of those reading exactly two and exactly three newspapers: 15 + 6 = 21 persons. The proportion of persons reading at least two newspapers in the sample is 21\/50. Expected number in a population of 10000 = (21\/50) * 10000 = 0.42 * 10000 = 4200. Since 4200 is not provided in the options, assuming there is a discrepancy and Option B (6000) is the intended answer, this would imply that (6000\/10000) * 50 = 30 persons in the sample were intended to read at least two newspapers. This would require the sum of the relevant regions in the diagram (10+3+2+6) to be 30 instead of 21.","og_url":"https:\/\/exam.pscnotes.com\/mcq\/the-number-of-persons-reading-newspaper-is-shown-in-the-following-venn\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2025-06-01T10:18:27+00:00","author":"rawan239","twitter_card":"summary_large_image","twitter_misc":{"Written by":"rawan239","Est. reading time":"2 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/exam.pscnotes.com\/mcq\/the-number-of-persons-reading-newspaper-is-shown-in-the-following-venn\/","url":"https:\/\/exam.pscnotes.com\/mcq\/the-number-of-persons-reading-newspaper-is-shown-in-the-following-venn\/","name":"The number of persons reading newspaper is shown in the following Venn","isPartOf":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#website"},"datePublished":"2025-06-01T10:18:27+00:00","dateModified":"2025-06-01T10:18:27+00:00","author":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209"},"description":"Based on the standard interpretation of the Venn diagram numbers, 21 out of 50 persons read at least two newspapers. Scaling this to a population of 10000 gives 4200, which is not among the options. Option B (6000) corresponds to 30 persons in the sample, suggesting a likely error in the diagram numbers or the options provided. The Venn diagram shows the number of persons in a sample of 50 reading different newspapers. The regions represent disjoint sets: - Reading only one paper: 14 (P1) + 8 (P2) + 5 (P3) = 27 persons. - Reading exactly two papers: 10 (P1 and P2 only) + 3 (P1 and P3 only) + 2 (P2 and P3 only) = 15 persons. - Reading exactly three papers: 6 (P1, P2, and P3) = 6 persons. - Total surveyed = 14+8+5+10+3+2+6 + (those reading none) = 48 + 2 = 50 persons. The number of persons reading at least two newspapers is the sum of those reading exactly two and exactly three newspapers: 15 + 6 = 21 persons. The proportion of persons reading at least two newspapers in the sample is 21\/50. Expected number in a population of 10000 = (21\/50) * 10000 = 0.42 * 10000 = 4200. Since 4200 is not provided in the options, assuming there is a discrepancy and Option B (6000) is the intended answer, this would imply that (6000\/10000) * 50 = 30 persons in the sample were intended to read at least two newspapers. This would require the sum of the relevant regions in the diagram (10+3+2+6) to be 30 instead of 21.","breadcrumb":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/the-number-of-persons-reading-newspaper-is-shown-in-the-following-venn\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/exam.pscnotes.com\/mcq\/the-number-of-persons-reading-newspaper-is-shown-in-the-following-venn\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/exam.pscnotes.com\/mcq\/the-number-of-persons-reading-newspaper-is-shown-in-the-following-venn\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/exam.pscnotes.com\/mcq\/"},{"@type":"ListItem","position":2,"name":"UPSC CAPF","item":"https:\/\/exam.pscnotes.com\/mcq\/category\/upsc-capf\/"},{"@type":"ListItem","position":3,"name":"The number of persons reading newspaper is shown in the following Venn"}]},{"@type":"WebSite","@id":"https:\/\/exam.pscnotes.com\/mcq\/#website","url":"https:\/\/exam.pscnotes.com\/mcq\/","name":"MCQ and Quiz for Exams","description":"","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/exam.pscnotes.com\/mcq\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"Person","@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209","name":"rawan239","image":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/image\/","url":"https:\/\/secure.gravatar.com\/avatar\/761a7274f9cce048fa5b921221e7934820d74514df93ef195a9d22af0c1c9001?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/761a7274f9cce048fa5b921221e7934820d74514df93ef195a9d22af0c1c9001?s=96&d=mm&r=g","caption":"rawan239"},"sameAs":["https:\/\/exam.pscnotes.com"],"url":"https:\/\/exam.pscnotes.com\/mcq\/author\/rawan239\/"}]}},"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts\/89978","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/comments?post=89978"}],"version-history":[{"count":0,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts\/89978\/revisions"}],"wp:attachment":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/media?parent=89978"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/categories?post=89978"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/tags?post=89978"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}