{"id":3398,"date":"2025-06-07T12:05:52","date_gmt":"2025-06-07T12:05:52","guid":{"rendered":"https:\/\/diznr.com\/?p=3398"},"modified":"2025-06-07T12:05:52","modified_gmt":"2025-06-07T12:05:52","slug":"general-aptitude-questions-and-answers-for-gate-cseit-gate-2020-the-probabilities-that-student-a","status":"publish","type":"post","link":"https:\/\/www.reilsolar.com\/pdf\/general-aptitude-questions-and-answers-for-gate-cseit-gate-2020-the-probabilities-that-student-a\/","title":{"rendered":"General Aptitude Questions and Answers for Gate CSEIT &#8211; GATE 2025 The probabilities that a student"},"content":{"rendered":"<p>General Aptitude Questions and Answers for Gate CSEIT &#8211; GATE 2025 The probabilities that a student<\/p>\n<p>[fvplayer id=&#8221;387&#8243;]<\/p>\n<p>Could you please provide the full question? It looks like it got cut off. I&#8217;ll be happy to help with the solution!<\/p>\n<h3><a href=\"https:\/\/www.iitiansgateclasses.com\/Document\/igc_gate_aptitude_probability.pdf\" target=\"_blank\" rel=\"noopener\">General Aptitude Questions and Answers for Gate CSEIT &#8211; GATE 2025 The probabilities that a student<\/a><\/h3>\n<h3 class=\"LC20lb MBeuO DKV0Md\"><a href=\"https:\/\/static.collegedekho.com\/media\/uploads\/2025\/02\/27\/1735purl_me-memory-gate-2025-sol.pdf\" target=\"_blank\" rel=\"noopener\">ME memory based GATE 2025_Forenoon.pmd<\/a><\/h3>\n<p data-start=\"0\" data-end=\"74\"><span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem] transition-colors duration-100 ease-in-out\">Here&#8217;s a classic probability question frequently encountered in GATE General Aptitude sections:<\/span><\/p>\n<hr data-start=\"76\" data-end=\"79\" \/>\n<h3 data-start=\"81\" data-end=\"98\"><strong data-start=\"85\" data-end=\"98\">Question:<\/strong><\/h3>\n<p data-start=\"100\" data-end=\"214\"><span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem] transition-colors duration-100 ease-in-out\">A student has the following probabilities of passing in three subjects: Mathematics (m), Physics (p), and Chemistry (c).<\/span> <span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem] transition-colors duration-100 ease-in-out\">The probabilities are such that:<\/span><span class=\"ms-1 inline-flex max-w-full items-center relative top-[-0.094rem] animate-[show_150ms_ease-in]\"><span class=\"relative start-0 bottom-0 flex h-full w-full items-center\"><span class=\"flex h-4 w-full items-center justify-between overflow-hidden\"><span class=\"max-w-full grow truncate overflow-hidden text-center\">Testbook<\/span><\/span><\/span><\/span><\/p>\n<ul data-start=\"216\" data-end=\"380\">\n<li data-start=\"216\" data-end=\"257\">\n<p data-start=\"218\" data-end=\"257\"><span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem] transition-colors duration-100 ease-in-out\">The probability of passing in <strong data-start=\"30\" data-end=\"46\">at least one<\/strong> subject is 75% (0.75).<\/span><\/p>\n<\/li>\n<li data-start=\"258\" data-end=\"299\">\n<p data-start=\"260\" data-end=\"299\"><span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem] transition-colors duration-100 ease-in-out\">The probability of passing in <strong data-start=\"30\" data-end=\"46\">at least two<\/strong> subjects is 50% (0.50).<\/span><\/p>\n<\/li>\n<li data-start=\"300\" data-end=\"380\">\n<p data-start=\"302\" data-end=\"380\"><span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem] transition-colors duration-100 ease-in-out\">The probability of passing in <strong data-start=\"30\" data-end=\"45\">exactly two<\/strong> subjects is 40% (0.40).<\/span><\/p>\n<\/li>\n<\/ul>\n<p data-start=\"382\" data-end=\"460\"><span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem] transition-colors duration-100 ease-in-out\">Based on this information, which of the following relations among m, p, and c are correct?<\/span><\/p>\n<p data-start=\"462\" data-end=\"474\"><strong data-start=\"462\" data-end=\"474\">Options:<\/strong><\/p>\n<p data-start=\"476\" data-end=\"650\">I. <span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem] transition-colors duration-100 ease-in-out\"><span class=\"katex\"><span class=\"katex-mathml\">m+p+c=2720m + p + c = \\frac{27}{20}<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">m<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">p<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">c<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">20<\/span><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">27<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><br data-start=\"518\" data-end=\"521\" \/>II. <span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem] transition-colors duration-100 ease-in-out\"><span class=\"katex\"><span class=\"katex-mathml\">m+p+c=1320m + p + c = \\frac{13}{20}<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">m<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">p<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">c<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">20<\/span><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">13<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><br data-start=\"564\" data-end=\"567\" \/>III. <span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem] transition-colors duration-100 ease-in-out\"><span class=\"katex\"><span class=\"katex-mathml\">m\u00d7p\u00d7c=110m \\times p \\times c = \\frac{1}{10}<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">m<\/span><span class=\"mbin\">\u00d7<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">p<\/span><span class=\"mbin\">\u00d7<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">c<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">10<\/span><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<hr data-start=\"652\" data-end=\"655\" \/>\n<h3 data-start=\"657\" data-end=\"674\"><strong data-start=\"661\" data-end=\"674\">Solution:<\/strong><\/h3>\n<p data-start=\"676\" data-end=\"725\">To analyze the given probabilities, let&#8217;s denote:<\/p>\n<ul data-start=\"727\" data-end=\"891\">\n<li data-start=\"727\" data-end=\"768\">\n<p data-start=\"729\" data-end=\"768\"><span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem] transition-colors duration-100 ease-in-out\"><span class=\"katex\"><span class=\"katex-mathml\">P(A)P(A)<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span>: Probability of passing in Mathematics = m<\/span><\/p>\n<\/li>\n<li data-start=\"769\" data-end=\"810\">\n<p data-start=\"771\" data-end=\"810\"><span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem] transition-colors duration-100 ease-in-out\"><span class=\"katex\"><span class=\"katex-mathml\">P(B)P(B)<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">B<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span>: Probability of passing in Physics = p<\/span><\/p>\n<\/li>\n<li data-start=\"811\" data-end=\"891\">\n<p data-start=\"813\" data-end=\"891\"><span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem] transition-colors duration-100 ease-in-out\"><span class=\"katex\"><span class=\"katex-mathml\">P(C)P(C)<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">C<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span>: Probability of passing in Chemistry = c<\/span><\/p>\n<\/li>\n<\/ul>\n<p data-start=\"893\" data-end=\"971\"><span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem] transition-colors duration-100 ease-in-out\">The probability of passing in at least one subject is given by:<\/span><\/p>\n<p><span class=\"katex-error\" title=\"ParseError: KaTeX parse error: Can't use function '\\]' in math mode at position 41: \u2026:50]{index=50} \\\u0332]\u0332:contentReferen\u2026\">:contentReference[oaicite:50]{index=50} \\]:contentReference[oaicite:52]{index=52} :contentReference[oaicite:54]{index=54}:contentReference[oaicite:56]{index=56} \\[ :contentReference[oaicite:58]{index=58} \\]:contentReference[oaicite:60]{index=60} :contentReference[oaicite:62]{index=62}:contentReference[oaicite:64]{index=64} \\[ :contentReference[oaicite:66]{index=66} \\]:contentReference[oaicite:68]{index=68} :contentReference[oaicite:70]{index=70}:contentReference[oaicite:72]{index=72} \\[ :contentReference[oaicite:74]{index=74} \\]:contentReference[oaicite:76]{index=76} :contentReference[oaicite:78]{index=78}:contentReference[oaicite:80]{index=80} \\[ :contentReference[oaicite:82]{index=82} \\]:contentReference[oaicite:84]{index=84} :contentReference[oaicite:86]{index=86}:contentReference[oaicite:88]{index=88} \\[ :contentReference[oaicite:90]{index=90} \\]:contentReference[oaicite:92]{index=92} :contentReference[oaicite:94]{index=94}:contentReference[oaicite:96]{index=96} :contentReference[oaicite:98]{index=98}:contentReference[oaicite:100]{index=100} &#8212; ### **Answer:** :contentReference[oaicite:102]{index=102}:contentReference[oaicite:104]{index=104} &#8212; :contentReference[oaicite:106]{index=106}:contentReference[oaicite:108]{index=108} &#8211; [Probability \u2013 Aptitude Questions and Answers | GeeksforGeeks](https:\/\/www.geeksforgeeks.org\/probability-questions\/) &#8211; [Probability GATE Questions &#8211; BYJU&#8217;S](https:\/\/byjus.com\/gate\/probability-gate-questions\/) &#8211; [GATE Questions on Probability &#8211; Testbook.com](https:\/\/testbook.com\/gate\/probability-gate-questions) :contentReference[oaicite:110]{index=110}:contentReference[oaicite:112]{index=112} ::contentReference[oaicite:113]{index=113}<\/span><\/p>\n<h2>GATE 2025 CSE Slot 1 Question Paper with Solutions PDF<\/h2>\n<div class=\"table-responsive\">\n<table class=\"table table-striped style_table\">\n<tbody>\n<tr>\n<td>GATE 2025 CSE Slot 1 Question Paper with Answer Key<\/td>\n<td><a href=\"https:\/\/assets.collegedunia.com\/public\/image\/CS1_1__7e36fe205ed31aade0093d7c49d65332.pdf\" target=\"_blank\" rel=\"noopener\"><img loading=\"lazy\" decoding=\"async\" class=\"no-zoom lazyloaded\" src=\"https:\/\/www.reilsolar.com\/pdf\/wp-content\/uploads\/sites\/2\/2025\/05\/Download_07111906e10ab418751c7d9f19d28049.png\" alt=\"download icon\" width=\"25\" height=\"25\" data-src=\"https:\/\/www.reilsolar.com\/pdf\/wp-content\/uploads\/sites\/2\/2025\/05\/Download_07111906e10ab418751c7d9f19d28049.png\" data-loaded=\"true\" \/><\/a><a href=\"https:\/\/assets.collegedunia.com\/public\/image\/CS1_1__7e36fe205ed31aade0093d7c49d65332.pdf\" target=\"_blank\" rel=\"nofollow noopener\">Download<\/a><\/td>\n<td><a href=\"https:\/\/assets.collegedunia.com\/public\/image\/GATE_2025_COMPUTER_SCIENCE_5__879c08c4317d00b36568ed7a3d567644.pdf\" target=\"_blank\" rel=\"nofollow noopener\">Check Solutions<\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>General Aptitude Questions and Answers for Gate CSEIT &#8211; GATE 2025 The probabilities that a student [fvplayer id=&#8221;387&#8243;] Could you please provide the full question? It looks like it got cut off. I&#8217;ll be happy to help with the solution! General Aptitude Questions and Answers for Gate CSEIT &#8211; GATE 2025 The probabilities that a [&hellip;]<\/p>\n","protected":false},"author":66,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[13],"tags":[],"class_list":["post-3398","post","type-post","status-publish","format-standard","hentry","category-general-aptitude"],"_links":{"self":[{"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/posts\/3398","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/users\/66"}],"replies":[{"embeddable":true,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/comments?post=3398"}],"version-history":[{"count":0,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/posts\/3398\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/media?parent=3398"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/categories?post=3398"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/tags?post=3398"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}