{"id":90724,"date":"2025-06-01T10:35:23","date_gmt":"2025-06-01T10:35:23","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=90724"},"modified":"2025-06-01T10:35:23","modified_gmt":"2025-06-01T10:35:23","slug":"a-coin-is-tossed-3-times-the-probability-of-getting-exactly-2-heads","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/a-coin-is-tossed-3-times-the-probability-of-getting-exactly-2-heads\/","title":{"rendered":"A coin is tossed 3 times. The probability of getting exactly 2 heads"},"content":{"rendered":"<p>A coin is tossed 3 times. The probability of getting exactly 2 heads is<\/p>\n<p>[amp_mcq option1=&#8221;$\\frac{1}{3}$&#8221; option2=&#8221;$\\frac{3}{8}$&#8221; option3=&#8221;$\\frac{1}{2}$&#8221; option4=&#8221;$\\frac{5}{8}$&#8221; correct=&#8221;option2&#8243;]<\/p>\n<div class=\"psc-box-pyq-exam-year-detail\">\n<div class=\"pyq-exam\">\n<div class=\"psc-heading\">This question was previously asked in<\/div>\n<div class=\"psc-title line-ellipsis\">UPSC CAPF &#8211; 2022<\/div>\n<\/div>\n<div class=\"pyq-exam-psc-buttons\"><a href=\"\/pyq\/pyq-upsc-capf-2022.pdf\" target=\"_blank\" class=\"psc-pdf-button\" rel=\"noopener\">Download PDF<\/a><a href=\"\/pyq-upsc-capf-2022\" target=\"_blank\" class=\"psc-attempt-button\" rel=\"noopener\">Attempt Online<\/a><\/div>\n<\/div>\n<section id=\"pyq-correct-answer\">\nWhen a fair coin is tossed, there are two possible outcomes: Heads (H) or Tails (T). When tossed 3 times, the total number of possible outcomes is 2\u00b3 = 8. The sample space is {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}. We are interested in the outcomes with exactly 2 heads. These are {HHT, HTH, THH}. There are 3 favorable outcomes. The probability of getting exactly 2 heads is the number of favorable outcomes divided by the total number of outcomes: 3\/8.<br \/>\n<\/section>\n<section id=\"pyq-key-points\">\n&#8211; List all possible outcomes (sample space) for the given number of trials.<br \/>\n&#8211; Identify the outcomes that satisfy the condition (favorable outcomes).<br \/>\n&#8211; Probability = (Number of favorable outcomes) \/ (Total number of outcomes).<br \/>\n&#8211; For independent events like coin tosses, the total number of outcomes for &#8216;n&#8217; trials is 2^n.<br \/>\n<\/section>\n<section id=\"pyq-additional-information\">\nThis type of problem can also be solved using the binomial probability formula: P(X=k) = C(n, k) * p^k * (1-p)^(n-k), where n is the number of trials (3), k is the number of successes (2 heads), p is the probability of success on a single trial (0.5 for heads), and C(n, k) is the binomial coefficient &#8220;n choose k&#8221;.<br \/>\nC(3, 2) = 3! \/ (2! * 1!) = 3.<br \/>\nP(exactly 2 heads) = C(3, 2) * (0.5)\u00b2 * (0.5)\u00b9 = 3 * 0.25 * 0.5 = 3 * 0.125 = 0.375 = 3\/8.<br \/>\n<\/section>\n","protected":false},"excerpt":{"rendered":"<p>A coin is tossed 3 times. The probability of getting exactly 2 heads is [amp_mcq option1=&#8221;$\\frac{1}{3}$&#8221; option2=&#8221;$\\frac{3}{8}$&#8221; option3=&#8221;$\\frac{1}{2}$&#8221; option4=&#8221;$\\frac{5}{8}$&#8221; correct=&#8221;option2&#8243;] This question was previously asked in UPSC CAPF &#8211; 2022 Download PDFAttempt Online When a fair coin is tossed, there are two possible outcomes: Heads (H) or Tails (T). When tossed 3 times, the total &#8230; <\/p>\n<p class=\"read-more-container\"><a title=\"A coin is tossed 3 times. The probability of getting exactly 2 heads\" class=\"read-more button\" href=\"https:\/\/exam.pscnotes.com\/mcq\/a-coin-is-tossed-3-times-the-probability-of-getting-exactly-2-heads\/#more-90724\">Detailed Solution<span class=\"screen-reader-text\">A coin is tossed 3 times. The probability of getting exactly 2 heads<\/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":[1108,1102],"class_list":["post-90724","post","type-post","status-publish","format-standard","hentry","category-upsc-capf","tag-1108","tag-quantitative-aptitude-and-reasoning","no-featured-image-padding"],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v22.2 (Yoast SEO v23.3) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>A coin is tossed 3 times. The probability of getting exactly 2 heads<\/title>\n<meta name=\"description\" content=\"When a fair coin is tossed, there are two possible outcomes: Heads (H) or Tails (T). When tossed 3 times, the total number of possible outcomes is 2\u00b3 = 8. The sample space is {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}. We are interested in the outcomes with exactly 2 heads. These are {HHT, HTH, THH}. There are 3 favorable outcomes. The probability of getting exactly 2 heads is the number of favorable outcomes divided by the total number of outcomes: 3\/8. - List all possible outcomes (sample space) for the given number of trials. - Identify the outcomes that satisfy the condition (favorable outcomes). - Probability = (Number of favorable outcomes) \/ (Total number of outcomes). - For independent events like coin tosses, the total number of outcomes for &#039;n&#039; trials is 2^n.\" \/>\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\/a-coin-is-tossed-3-times-the-probability-of-getting-exactly-2-heads\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"A coin is tossed 3 times. The probability of getting exactly 2 heads\" \/>\n<meta property=\"og:description\" content=\"When a fair coin is tossed, there are two possible outcomes: Heads (H) or Tails (T). When tossed 3 times, the total number of possible outcomes is 2\u00b3 = 8. The sample space is {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}. We are interested in the outcomes with exactly 2 heads. These are {HHT, HTH, THH}. There are 3 favorable outcomes. The probability of getting exactly 2 heads is the number of favorable outcomes divided by the total number of outcomes: 3\/8. - List all possible outcomes (sample space) for the given number of trials. - Identify the outcomes that satisfy the condition (favorable outcomes). - Probability = (Number of favorable outcomes) \/ (Total number of outcomes). - For independent events like coin tosses, the total number of outcomes for &#039;n&#039; trials is 2^n.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/a-coin-is-tossed-3-times-the-probability-of-getting-exactly-2-heads\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2025-06-01T10:35:23+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=\"1 minute\" \/>\n<!-- \/ Yoast SEO Premium plugin. -->","yoast_head_json":{"title":"A coin is tossed 3 times. The probability of getting exactly 2 heads","description":"When a fair coin is tossed, there are two possible outcomes: Heads (H) or Tails (T). When tossed 3 times, the total number of possible outcomes is 2\u00b3 = 8. The sample space is {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}. We are interested in the outcomes with exactly 2 heads. These are {HHT, HTH, THH}. There are 3 favorable outcomes. The probability of getting exactly 2 heads is the number of favorable outcomes divided by the total number of outcomes: 3\/8. - List all possible outcomes (sample space) for the given number of trials. - Identify the outcomes that satisfy the condition (favorable outcomes). - Probability = (Number of favorable outcomes) \/ (Total number of outcomes). - For independent events like coin tosses, the total number of outcomes for 'n' trials is 2^n.","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\/a-coin-is-tossed-3-times-the-probability-of-getting-exactly-2-heads\/","og_locale":"en_US","og_type":"article","og_title":"A coin is tossed 3 times. The probability of getting exactly 2 heads","og_description":"When a fair coin is tossed, there are two possible outcomes: Heads (H) or Tails (T). When tossed 3 times, the total number of possible outcomes is 2\u00b3 = 8. The sample space is {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}. We are interested in the outcomes with exactly 2 heads. These are {HHT, HTH, THH}. There are 3 favorable outcomes. The probability of getting exactly 2 heads is the number of favorable outcomes divided by the total number of outcomes: 3\/8. - List all possible outcomes (sample space) for the given number of trials. - Identify the outcomes that satisfy the condition (favorable outcomes). - Probability = (Number of favorable outcomes) \/ (Total number of outcomes). - For independent events like coin tosses, the total number of outcomes for 'n' trials is 2^n.","og_url":"https:\/\/exam.pscnotes.com\/mcq\/a-coin-is-tossed-3-times-the-probability-of-getting-exactly-2-heads\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2025-06-01T10:35:23+00:00","author":"rawan239","twitter_card":"summary_large_image","twitter_misc":{"Written by":"rawan239","Est. reading time":"1 minute"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/exam.pscnotes.com\/mcq\/a-coin-is-tossed-3-times-the-probability-of-getting-exactly-2-heads\/","url":"https:\/\/exam.pscnotes.com\/mcq\/a-coin-is-tossed-3-times-the-probability-of-getting-exactly-2-heads\/","name":"A coin is tossed 3 times. The probability of getting exactly 2 heads","isPartOf":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#website"},"datePublished":"2025-06-01T10:35:23+00:00","dateModified":"2025-06-01T10:35:23+00:00","author":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209"},"description":"When a fair coin is tossed, there are two possible outcomes: Heads (H) or Tails (T). When tossed 3 times, the total number of possible outcomes is 2\u00b3 = 8. The sample space is {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}. We are interested in the outcomes with exactly 2 heads. These are {HHT, HTH, THH}. There are 3 favorable outcomes. The probability of getting exactly 2 heads is the number of favorable outcomes divided by the total number of outcomes: 3\/8. - List all possible outcomes (sample space) for the given number of trials. - Identify the outcomes that satisfy the condition (favorable outcomes). - Probability = (Number of favorable outcomes) \/ (Total number of outcomes). - For independent events like coin tosses, the total number of outcomes for 'n' trials is 2^n.","breadcrumb":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/a-coin-is-tossed-3-times-the-probability-of-getting-exactly-2-heads\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/exam.pscnotes.com\/mcq\/a-coin-is-tossed-3-times-the-probability-of-getting-exactly-2-heads\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/exam.pscnotes.com\/mcq\/a-coin-is-tossed-3-times-the-probability-of-getting-exactly-2-heads\/#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":"A coin is tossed 3 times. 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