{"id":20333,"date":"2024-04-15T05:51:28","date_gmt":"2024-04-15T05:51:28","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=20333"},"modified":"2024-04-15T05:51:28","modified_gmt":"2024-04-15T05:51:28","slug":"a-box-contains-4-white-balls-and-3-red-balls-in-succession-two-balls-are-randomly-selected-and-removed-from-the-box-give-that-the-first-removed-ball-is-white-the-probability-that-the-second-remove","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/a-box-contains-4-white-balls-and-3-red-balls-in-succession-two-balls-are-randomly-selected-and-removed-from-the-box-give-that-the-first-removed-ball-is-white-the-probability-that-the-second-remove\/","title":{"rendered":"A box contains 4 white balls and 3 red balls. In succession, two balls are randomly selected and removed from the box. Give that the first removed ball is white, the probability that the second removed ball is red is A. $$\\frac{1}{3}$$ B. $$\\frac{3}{7}$$ C. $$\\frac{1}{2}$$ D. $$\\frac{4}{7}$$"},"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_6a987b5e3512f\">\r\n                                            <div class=\"option\" data-option-key=\"option1\" data-is-correct=\"false\">\r\n                    $$\frac{1}{3}$$                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option2\" data-is-correct=\"false\">\r\n                    $$\frac{3}{7}$$                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option3\" data-is-correct=\"true\">\r\n                    $$\frac{1}{2}$$                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option4\" data-is-correct=\"false\">\r\n                    $$\frac{4}{7}$$                <\/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 $\\boxed{\\frac{3}{7}}$.<\/p>\n<p>The probability of event A happening, given that event B has already happened, is called the conditional probability of A given B, and is denoted by $P(A|B)$. It can be calculated using the following formula:<\/p>\n<p>$$P(A|B) = \\frac{P(A \\cap B)}{P(B)}$$<\/p>\n<p>In this case, event A is the event that the second ball removed is red, and event B is the event that the first ball removed is white. We are given that event B has already happened, so we need to calculate $P(A \\cap B)$ and $P(B)$.<\/p>\n<p>$P(A \\cap B)$ is the probability that both the first ball removed is white and the second ball removed is red. This can be calculated as follows:<\/p>\n<p>$$P(A \\cap B) = \\frac{4}{7} \\times \\frac{3}{6} = \\frac{2}{7}$$<\/p>\n<p>$P(B)$ is the probability that the first ball removed <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        <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>     Subscribe on YouTube\r\n        <\/a>\r\n    <\/div> is white. This can be calculated as follows:<\/p>\n<p>$$P(B) = \\frac{4}{7}$$<\/p>\n<p>Therefore, the conditional probability that the second ball removed is red, given that the first ball removed is white, is:<\/p>\n<p>$$P(A|B) = \\frac{P(A \\cap B)}{P(B)} = \\frac{\\frac{2}{7}}{\\frac{4}{7}} = \\frac{3}{7}$$<\/p>\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>A box contains 4 white balls and 3 red balls. In succession, two balls are randomly selected and removed from the box. Give that the first removed ball is white, the probability that the second removed ball is red is A. $$\\frac{1}{3}$$ B. $$\\frac{3}{7}$$ C. $$\\frac{1}{2}$$ D. $$\\frac{4}{7}$$<\/title>\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-box-contains-4-white-balls-and-3-red-balls-in-succession-two-balls-are-randomly-selected-and-removed-from-the-box-give-that-the-first-removed-ball-is-white-the-probability-that-the-second-remove\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"A box contains 4 white balls and 3 red balls. In succession, two balls are randomly selected and removed from the box. 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In succession, two balls are randomly selected and removed from the box. Give that the first removed ball is white, the probability that the second removed ball is red is A. $$\\frac{1}{3}$$ B. $$\\frac{3}{7}$$ C. $$\\frac{1}{2}$$ D. $$\\frac{4}{7}$$","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-box-contains-4-white-balls-and-3-red-balls-in-succession-two-balls-are-randomly-selected-and-removed-from-the-box-give-that-the-first-removed-ball-is-white-the-probability-that-the-second-remove\/","og_locale":"en_US","og_type":"article","og_title":"A box contains 4 white balls and 3 red balls. In succession, two balls are randomly selected and removed from the box. 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