{"id":20332,"date":"2024-04-15T05:51:28","date_gmt":"2024-04-15T05:51:28","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=20332"},"modified":"2024-04-15T05:51:28","modified_gmt":"2024-04-15T05:51:28","slug":"two-white-and-two-black-balls-kept-in-two-bins-are-arranged-in-four-ways-as-shown-below-in-each-arrangement-a-bin-has-to-be-chosen-randomly-and-only-one-ball-needs-to-be-picked-randomly-from-the-ch","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/two-white-and-two-black-balls-kept-in-two-bins-are-arranged-in-four-ways-as-shown-below-in-each-arrangement-a-bin-has-to-be-chosen-randomly-and-only-one-ball-needs-to-be-picked-randomly-from-the-ch\/","title":{"rendered":"Two white and two black balls, kept in two bins are arranged in four ways as shown below. In each arrangement, a bin has to be chosen randomly and only one ball needs to be picked randomly from the chosen bin. Which one of the following arrangements has the highest probability for getting a white face picked? A. B. C. D."},"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_6a9880fea5d7c\">\r\n                                            <div class=\"option\" data-option-key=\"option1\" data-is-correct=\"false\">\r\n                    nan                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option2\" data-is-correct=\"false\">\r\n                    nan                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option3\" data-is-correct=\"false\">\r\n                    nan                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option4\" data-is-correct=\"true\">\r\n                    nan                <\/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 D.<\/p>\n<p>In arrangement D, there are two white balls in the first bin and one white ball in the second bin. When a bin is chosen randomly, the probability of choosing the first bin is $\\frac{1}{2}$. When the first bin is chosen, the probability of picking a white ball is $\\frac{2}{3}$. Therefore, the overall probability of picking a white ball in arrangement D <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 <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> 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 $\\frac{1}{2} \\times \\frac{2}{3} = \\frac{2}{3}$.<\/p>\n<p>In arrangement A, there is one white ball in each bin. When a bin is chosen randomly, the probability of choosing either bin is $\\frac{1}{2}$. When either bin is chosen, the probability of picking a white ball is $\\frac{1}{2}$. Therefore, the overall probability of picking a white ball in arrangement A is $\\frac{1}{2} \\times \\frac{1}{2} = \\frac{1}{4}$.<\/p>\n<p>In arrangement B, there are two white balls in the second bin and one white ball in the first bin. When a bin is chosen randomly, the probability of choosing the second bin is $\\frac{1}{2}$. When the second bin is chosen, the probability of picking a white ball is $\\frac{2}{3}$. Therefore, the overall probability of picking a white ball in arrangement B is $\\frac{1}{2} \\times \\frac{2}{3} = \\frac{1}{3}$.<\/p>\n<p>In arrangement C, there is one white ball in each bin. When a bin is chosen randomly, the probability of choosing either bin is $\\frac{1}{2}$. When either bin is chosen, the probability of picking a white ball is $\\frac{1}{2}$. Therefore, the overall probability of picking a white ball in arrangement C is $\\frac{1}{2} \\times \\frac{1}{2} = \\frac{1}{4}$.<\/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>Two white and two black balls, kept in two bins are arranged in four ways as shown below. In each arrangement, a bin has to be chosen randomly and only one ball needs to be picked randomly from the chosen bin. Which one of the following arrangements has the highest probability for getting a white face picked? A. B. C. 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