{"id":20339,"date":"2024-04-15T05:51:34","date_gmt":"2024-04-15T05:51:34","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=20339"},"modified":"2024-04-15T05:51:34","modified_gmt":"2024-04-15T05:51:34","slug":"an-unbiased-coin-is-tossed-five-times-the-outcome-of-each-toss-is-either-a-head-or-a-tail-the-probability-of-getting-at-least-one-head-is-a-frac132-b-frac1332-c-frac","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/an-unbiased-coin-is-tossed-five-times-the-outcome-of-each-toss-is-either-a-head-or-a-tail-the-probability-of-getting-at-least-one-head-is-a-frac132-b-frac1332-c-frac\/","title":{"rendered":"An unbiased coin is tossed five times. The outcome of each toss is either a head or a tail. The probability of getting at least one head is A. $$\\frac{1}{{32}}$$ B. $$\\frac{{13}}{{32}}$$ C. $$\\frac{{16}}{{32}}$$ D. $$\\frac{{31}}{{32}}$$"},"content":{"rendered":"<p>\r\n    <!-- Check if it's an AMP page -->\r\n            <!-- Non-AMP version -->\r\n        <div class=\"mcq-container\" data-quiz-id=\"quizState_6a9817d9a762f\">\r\n                                            <div class=\"option\" data-option-key=\"option1\" data-is-correct=\"true\">\r\n                    $$\frac{1}{{32}}$$                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option2\" data-is-correct=\"false\">\r\n                    $$\frac{{13}}{{32}}$$                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option3\" data-is-correct=\"false\">\r\n                    $$\frac{{16}}{{32}}$$                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option4\" data-is-correct=\"false\">\r\n                    $$\frac{{31}}{{32}}$$                <\/div>\r\n                            \r\n            <!-- Feedback messages for non-AMP -->\r\n            <div class=\"feedback\" data-feedback=\"wrong\">Answer is Right!<\/div>\r\n            <div class=\"feedback\" data-feedback=\"right\">Answer is Wrong!<\/div>\r\n        <\/div>\r\n\r\n        <script>\r\n        document.addEventListener('DOMContentLoaded', function () {\r\n            var containers = document.querySelectorAll('.mcq-container');\r\n\r\n            containers.forEach(function(container) {\r\n                var options = container.querySelectorAll('.option');\r\n                var feedbackSelect = container.querySelector('[data-feedback=\"select\"]');\r\n                var feedbackWrong = container.querySelector('[data-feedback=\"wrong\"]');\r\n                var feedbackRight = container.querySelector('[data-feedback=\"right\"]');\r\n\r\n                options.forEach(function(option) {\r\n                    option.addEventListener('click', function() {\r\n                        var selectedOption = option.getAttribute('data-option-key');\r\n                        var isCorrect = option.getAttribute('data-is-correct') === 'true';\r\n\r\n                        \/\/ Remove previous selections\r\n                        options.forEach(function(opt) {\r\n                            opt.classList.remove('correct', 'incorrect');\r\n                        });\r\n\r\n                        \/\/ Add the correct\/incorrect class\r\n                        if (isCorrect) {\r\n                            option.classList.add('correct');\r\n                            feedbackRight.hidden = false;\r\n                            feedbackWrong.hidden = true;\r\n                        } else {\r\n                            option.classList.add('incorrect');\r\n                            feedbackRight.hidden = true;\r\n                            feedbackWrong.hidden = false;\r\n                        }\r\n\r\n                        \/\/ Hide select feedback\r\n                        feedbackSelect.hidden = true;\r\n                    });\r\n                });\r\n            });\r\n        });\r\n        <\/script>\r\n    \r\n    <!--more--><\/p>\n<p>The correct answer is $\\boxed{\\frac{{16}}{{32}}}$.<\/p>\n<p>The probability of getting at least one head is the complement of the probability of getting no heads. The probability of getting no heads is the probability of getting tails all five times. This is $\\frac{1}{2}\\times\\frac{1}{2}\\times\\frac{1}{2}\\times\\frac{1}{2}\\times\\frac{1}{2} = \\frac{1}{32}$. Therefore, the probability of getting at least one head is $1 &#8211; \\frac{1}{32} = \\boxed{\\frac{{16}}{{32}}}$.<\/p>\n<p>Each option can be explained as follows:<\/p>\n<ul>\n<li>Option A: $\\frac{1}{{32}}$ is the probability of getting all tails. This is a very unlikely event, so it is not the correct answer.<\/li>\n<li>Option B: $\\frac{{13}}{{32}}$ is the probability of getting exactly one head. This is possible, but it is not as likely as getting at least one head. Therefore, it is not the correct answer.<\/li>\n<li>Option C: <div class=\"telegram-channel-container\">\r\n        <a href=\"https:\/\/t.me\/pscnotes2025\" target=\"_blank\" class=\"telegram-channel-button\">\r\n            <span class=\"telegram-icon\">\r\n                <svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" viewBox=\"0 0 496 512\">\r\n                    <path fill=\"white\" d=\"M248,8C111,8,0,119,0,256s111,248,248,248s248-111,248-248S385,8,248,8z M362,177L320,367c-3,14-10,18-20,14l-56-41l-27,26 c-3,3-5,5-10,5l4-63L323,196c5-5-1-7-8-3l-98,62l-42-13c-9-3-10-9,2-14l162-63C351,160,365,164,362,177z\"\/>\r\n                <\/svg>\r\n            <\/span>\r\n            Join Our Telegram Channel\r\n        <\/a>\r\n    <\/div> $\\frac{{16}}{{32}}$ is the probability of getting at least one head. This is the correct answer.<\/li>\n<li>Option D: $\\frac{{31}}{{32}}$ is the probability of getting all heads. This <div class=\"youtube-subscribe-container\">\r\n        <a href=\"https:\/\/www.youtube.com\/channel\/UCNHT8lW-JmLC68rjBfZhdkg?sub_confirmation=1\" target=\"_blank\" class=\"youtube-subscribe-button\">\r\n            <span class=\"youtube-icon\">\r\n                <svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" viewBox=\"0 0 576 512\">\r\n                    <path d=\"M549.7 124.1c-6.3-23.7-24.8-42.3-48.3-48.6C458.8 64 288 64 288 64S117.2 64 74.6 75.5c-23.5 6.3-42 24.9-48.3 48.6-11.4 42.9-11.4 132.3-11.4 132.3s0 89.4 11.4 132.3c6.3 23.7 24.8 41.5 48.3 47.8C117.2 448 288 448 288 448s170.8 0 213.4-11.5c23.5-6.3 42-24.2 48.3-47.8 11.4-42.9 11.4-132.3 11.4-132.3s0-89.4-11.4-132.3zm-317.5 213.5V175.2l142.7 81.2-142.7 81.2z\"\/>\r\n                <\/svg>\r\n            <\/span>\r\n            Subscribe on YouTube\r\n        <\/a>\r\n    <\/div> is a very unlikely event, so it is not the correct answer.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Join Our Telegram Channel Subscribe on YouTube<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[691],"tags":[],"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>An unbiased coin is tossed five times. 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