{"id":20329,"date":"2024-04-15T05:51:26","date_gmt":"2024-04-15T05:51:26","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=20329"},"modified":"2024-04-15T05:51:26","modified_gmt":"2024-04-15T05:51:26","slug":"a-box-has-8-red-balls-and-8-green-balls-two-balls-are-drawn-randomly-in-succession-from-the-box-without-replacement-the-probability-that-the-first-ball-drawn-is-red-and-the-second-ball-drawn-is-gree","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/a-box-has-8-red-balls-and-8-green-balls-two-balls-are-drawn-randomly-in-succession-from-the-box-without-replacement-the-probability-that-the-first-ball-drawn-is-red-and-the-second-ball-drawn-is-gree\/","title":{"rendered":"A box has 8 red balls and 8 green balls. Two balls are drawn randomly in succession from the box without replacement. The probability that the first ball drawn is red and the second ball drawn is green is A. $$\\frac{4}{{15}}$$ B. $$\\frac{7}{{16}}$$ C. $$\\frac{1}{2}$$ D. $$\\frac{8}{{15}}$$"},"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_6a98a6b46a6b2\">\r\n                                            <div class=\"option\" data-option-key=\"option1\" data-is-correct=\"false\">\r\n                    $$\frac{4}{{15}}$$                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option2\" data-is-correct=\"false\">\r\n                    $$\frac{7}{{16}}$$                <\/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                    $$\frac{8}{{15}}$$                <\/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 $\\boxed{\\frac{7}{16}}$.<\/p>\n<p>The probability of event A happening, then event B, is the probability of event A happening times the probability of event B happening given that event A already happened. In this case, event A is drawing a red ball and leaving it out, and event B is drawing a green ball.<\/p>\n<p>The probability of drawing a red ball is $\\frac{8}{16}$, because there are 8 red balls and 16 total balls.<\/p>\n<p>The probability of drawing a green ball after drawing a red ball is $\\frac{8}{15}$, because there are 8 green balls left and 15 total balls left.<\/p>\n<p>Therefore, the probability of drawing a red ball, then a green ball is $\\frac{8}{16} \\cdot \\frac{8}{15} = \\boxed{\\frac{7}{16}}$.<\/p>\n<p>Option A is incorrect because it is the probability of drawing a green ball, then a red ball. This is not the same as the probability of drawing a red ball, then a green ball.<\/p>\n<p>Option B is incorrect because it is the probability of drawing a red ball on the first draw. This is not the same as the probability of drawing a red ball, then a green ball.<\/p>\n<p>Option C is incorrect because it is the probability of drawing <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> a green ball on <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> the first draw, then a red ball on the second draw. This is not the same as the probability of drawing a red ball, then a green ball.<\/p>\n<p>Option D is incorrect because it is the probability of drawing a red ball or a green ball on the first draw, then a red ball or a green ball on the second draw. This is not the same as the probability of drawing a red ball, then a green ball.<\/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 has 8 red balls and 8 green balls. Two balls are drawn randomly in succession from the box without replacement. The probability that the first ball drawn is red and the second ball drawn is green is A. $$\\frac{4}{{15}}$$ B. $$\\frac{7}{{16}}$$ C. $$\\frac{1}{2}$$ D. $$\\frac{8}{{15}}$$<\/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-has-8-red-balls-and-8-green-balls-two-balls-are-drawn-randomly-in-succession-from-the-box-without-replacement-the-probability-that-the-first-ball-drawn-is-red-and-the-second-ball-drawn-is-gree\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"A box has 8 red balls and 8 green balls. Two balls are drawn randomly in succession from the box without replacement. 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