{"id":1501,"date":"2020-07-20T23:40:18","date_gmt":"2020-07-20T15:40:18","guid":{"rendered":"https:\/\/www.study-together.com\/edu\/?page_id=1501"},"modified":"2020-11-02T23:19:51","modified_gmt":"2020-11-02T15:19:51","slug":"probability","status":"publish","type":"page","link":"https:\/\/www.study-together.com\/edu\/secondary\/form3_maths\/probability\/","title":{"rendered":"11. \u6982\u7387 (Probability)"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-page\" data-elementor-id=\"1501\" class=\"elementor elementor-1501\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-9c56556 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"9c56556\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-66 elementor-top-column elementor-element elementor-element-0a4bab7\" data-id=\"0a4bab7\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-8af22ce elementor-widget elementor-widget-text-editor\" data-id=\"8af22ce\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<h2>11.1\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u6982\u7387\u7684\u8a08\u7b97<\/h2><p>\u6982\u7387\u662f\u7528\u4f86\u8868\u793a<strong>\u4e00\u4ef6\u4e8b\u4ef6\u767c\u751f\u7684\u53ef\u80fd\u6027<\/strong>\u3002\u8a2dE\u662f\u4e00\u4ef6\u4e8b\u4ef6\uff0c\u800cP(E)\u5247\u662f\u4e8b\u4ef6E\u767c\u751f\u7684\u6982\u7387\u3002\u9019\u57fa\u672c\u4e0a\u5c31\u662f\u6211\u5011\u5e73\u65e5\u6240\u8aaa\u7684\u300c\u6a5f\u6703\u7387\u300d\u3002<\/p><p>\u4f8b\u5982\u64f2\u9280\u4ed4\u64f2\u5f97\u201c\u516c\u201d\u7684\u6a5f\u6703\u7387\uff08\u6982\u7387\uff09\u662f1\/2\u53ef\u4ee5\u5beb\u6210\uff1a<\/p><ul><li style=\"list-style-type: none;\"><ul><li>P(\u64f2\u9280\u4ed4\u64f2\u5f97\u516c) = 1\/2<\/li><\/ul><\/li><\/ul><p>P(E) \u7684\u8a08\u7b97\u65b9\u6cd5\u5982\u4e0b\uff1a<\/p><ul><li style=\"list-style-type: none;\"><ul><li>\\(P(E) = \\dfrac{\u7b26\u5408\u4e8b\u4ef6E\u7684\u7d50\u679c\u7684\u6578\u76ee}{\u6240\u6709\u53ef\u80fd\u7d50\u679c\u7684\u6578\u76ee}\\)<\/li><\/ul><\/li><\/ul>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-84a32d0 elementor-widget elementor-widget-text-editor\" data-id=\"84a32d0\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<h2>11.2\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u6982\u7387\u7684\u6027\u8cea<\/h2><p>\u5c0d\u65bc\u4efb\u4f55\u4e00\u4ef6\u4e8b\u4ef6E\uff0c\u5b83\u767c\u751f\u7684\u6982\u7387P(E)\u6709\u4ee5\u4e0b\u6027\u8cea\uff1a<\/p><ul><li>\\(0 \\leqslant P(E) \\leqslant 1\\)<ul><li>\u7576P(E)\u8d8a\u5927\u6642\uff0cE\u767c\u751f\u7684\u6a5f\u6703\u8d8a\u5927\u3002<\/li><li>\u7576P(E) = 0\u6642\uff0c\u4e8b\u4ef6E\u662f\u4e00\u5b9a\u4e0d\u6703\u767c\u751f\u7684\u3002<\/li><li>\u7576P(E) = 1\u6642\uff0c\u4e8b\u4ef6E\u662f\u4e00\u5b9a\u6703\u767c\u751f\u7684\u3002<\/li><\/ul><\/li><li>\u5982\u679cE\u2019\u4ee3\u8868\u201c\u4e8b\u4ef6E\u4e0d\u6703\u767c\u751f\u201d\uff0c\u5247<br \/>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 P(E) + P(E\u2019) = 1<br \/>\u9019\u662f\u56e0\u70ba\u201cE\u4e00\u4fc2\u767c\u751f\uff0c\u4e00\u4fc2\u5514\u767c\u751f\u201d\u662f\u5fc5\u5b9a\u7684\u3002<\/li><\/ul>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-07bae70 elementor-widget elementor-widget-text-editor\" data-id=\"07bae70\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<h3>11.3\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u89e3\u984c\u6280\u5de7<\/h3><p>\u96d6\u7136\u5728\u8a08\u7b97\u6982\u7387\u6642\u6211\u5011\u53ef\u4ee5\u5229\u7528\u516c\u5f0f\uff1a<\/p><ul><li>\\(P(E) = \\dfrac{\u7b26\u5408\u4e8b\u4ef6E\u7684\u7d50\u679c\u7684\u6578\u76ee}{\u6240\u6709\u53ef\u80fd\u7d50\u679c\u7684\u6578\u76ee}\\)<\/li><\/ul><p>\u4f46\u5728\u89e3\u7b54\u4e00\u4e9b\u8f03\u8907\u96dc\u7684\u554f\u984c\u6642\uff0c\u6211\u5011\u4e26\u4e0d\u80fd\u5bb9\u6613\u5730\u6c42\u5f97\u201c\u6240\u6709\u53ef\u80fd\u7d50\u679c\u7684\u6578\u76ee\u201d\u548c\u201c\u7b26\u5408\u7684\u7d50\u679c\u7684\u6578\u76ee\u201d\u3002\u9019\u6642\u4fbf\u9700\u8981\u5229\u7528\u4ee5\u4e0b\u7684\u6280\u5de7\u4e86\u3002<\/p><h4>11.3.1\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u6a39\u5f62\u5716<\/h4><p>\u5229\u7528\u6a39\u5f62\u5716\uff0c\u6211\u5011\u53ef\u4ee5\u628a\u4e8b\u60c5\u6240\u6709\u53ef\u80fd\u7684\u7d50\u679c\u756b\u51fa\u4f86\u3002\u6a39\u5f62\u5716\u901a\u5e38\u662f\u7528\u5728\u201c\u6709\u4e00\u500b\u904e\u7a0b\u201d\u7684\u4e8b\u60c5\u4e0a\u3002<\/p><p>\u4f8b1\uff1a\u00a0\u00a0\u00a0 \u6c42\u64f2\u4e09\u6b21\u9280\u4ed4\u4e2d\u81f3\u5c11\u64f2\u5f97\u4e00\u500b\u516c\u7684\u6982\u7387\u3002<br \/>\u89e3\u7b54\uff1a\u00a0\u00a0 \u64f2\u4e09\u500b\u9280\u4ed4\u7684\u60c5\u6cc1\u53ef\u7528\u4ee5\u4e0b\u7684\u6a39\u5f62\u5716\u4f86\u8868\u793a\uff08H\u4ee3\u8868\u516c\uff1bT\u4ee3\u8868\u5b57\uff09\uff1a<\/p><p style=\"padding-left: 40px;\"><img fetchpriority=\"high\" decoding=\"async\" class=\"alignnone size-full wp-image-1610\" src=\"https:\/\/www.study-together.com\/edu\/wp-content\/uploads\/2020\/07\/f3maths_probTreeDaig.jpg\" alt=\"\u6982\u7387-\u6a39\u5f62\u5716\" width=\"416\" height=\"267\" srcset=\"https:\/\/www.study-together.com\/edu\/wp-content\/uploads\/2020\/07\/f3maths_probTreeDaig.jpg 416w, https:\/\/www.study-together.com\/edu\/wp-content\/uploads\/2020\/07\/f3maths_probTreeDaig-300x193.jpg 300w\" sizes=\"(max-width: 416px) 100vw, 416px\" \/><\/p><p>\u5047\u5982\u8981\u6c42\u300c\u64f2\u4e09\u6b21\u9280\u4ed4\u4e2d\u81f3\u5c11\u6709\u4e00\u500b\u516c\u300d\u7684\u6982\u7387\uff0c\u5229\u7528\u4ee5\u4e0a\u6a39\u5f62\u5716\uff0c\u6211\u5011\u53ef\u898b\u300c\u6240\u6709\u53ef\u80fd\u7684\u7d50\u679c\u7684\u6578\u76ee= 8\u300d\u53ca\u300c\u7b26\u5408\u81f3\u5c11\u6709\u4e00\u500b\u516c\u7684\u7d50\u679c\u7684\u6578\u76ee = 7\u300d\u3002\u00a0 <br \/>\u6240\u4ee5\uff0cP(\u64f2\u4e09\u6b21\u9280\u4ed4\u4e2d\u81f3\u5c11\u6709\u4e00\u500b\u516c) = 7 \/ 8\u3002<\/p><h4>11.3.2\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u5217\u8868<\/h4><p>\u5217\u8868\u901a\u5e38\u6bd4\u6a39\u5f62\u5716\u6574\u9f4a\u548c\u5bb9\u6613\u770b\u3002\u4f46\u662f\u56e0\u70ba\u4e00\u500b\u8868\u4e2d\u53ea\u6709\u300c\u5217\u300d\u548c\u300c\u6b04\u300d\uff0c\u6240\u4ee5\u53ea\u80fd\u7528\u4f86\u8868\u793a\u201c\u6709\u4e8c\u500b\u6b65\u9a5f\u201d\u7684\u4e8b\u60c5\uff08\u4f8b\u5982\u64f2\u5169\u7c92\u9ab0\uff09\u3002<\/p><p>\u4f8b2\uff1a\u00a0\u00a0\u00a0 \u6c42\u64f2\u5169\u7c92\u9ab0\u6642\u9ede\u6578\u4e4b\u7e3d\u548c\u70ba\uff15\u7684\u500d\u6578\u7684\u6982\u7387\u3002<br \/>\u89e3\u7b54\uff1a\u00a0\u00a0 \u64f2\u5169\u7c92\u9ab0\u7684\u9ede\u6578\u7e3d\u548c\u5217\u8868\u5982\u4e0b\uff1a<\/p><p style=\"padding-left: 80px;\"><img decoding=\"async\" class=\"alignnone size-full wp-image-1612\" src=\"https:\/\/www.study-together.com\/edu\/wp-content\/uploads\/2020\/07\/f3maths_probListTable.jpg\" alt=\"\u6982\u7387-\u5217\u8868\u6cd5\" width=\"462\" height=\"220\" srcset=\"https:\/\/www.study-together.com\/edu\/wp-content\/uploads\/2020\/07\/f3maths_probListTable.jpg 462w, https:\/\/www.study-together.com\/edu\/wp-content\/uploads\/2020\/07\/f3maths_probListTable-300x143.jpg 300w\" sizes=\"(max-width: 462px) 100vw, 462px\" \/><\/p><p style=\"padding-left: 40px;\">\u6839\u64da\u4e0a\u8868\uff0cP(\u64f2\u4e8c\u7c92\u9ab0\u6642\u9ede\u6578\u4e4b\u7e3d\u548c\u70ba5\u7684\u500d\u6578) =\\(\\dfrac{7}{36}\\)<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-eae486c elementor-widget elementor-widget-text-editor\" data-id=\"eae486c\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<h3>11.4\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u7406\u8ad6\u6982\u7387\u548c\u5be6\u9a57\u6982\u7387<\/h3><p>\u4ee5\u4e0a\u6240\u63d0\u53ca\u7684\u6982\u7387\u4e5f\u662f\u300c\u7406\u8ad6\u6982\u7387\u300d\uff0c\u5373\u5229\u7528\u908f\u8f2f\u63a8\u7406\u6240\u6c42\u5f97\u7684\u6982\u7387\u3002\u800c\u7684\u300c\u5be6\u9a57\u6982\u7387\u300d\u5c31\u662f\u900f\u904e\u5be6\u9a57\u53ca\u6578\u64da\u7684\u6536\u96c6\uff0c\u5229\u7528\u76f8\u5c0d\u983b\u6578\u6240\u6c42\u5f97\u7684\u6982\u7387\u3002<\/p><ul><li><span style=\"color: #ff0000;\">\u4e00\u822c\u8a08\u7b97\u6642\uff0c\u9664\u975e\u984c\u76ee\u6307\u660e\uff0c\u5426\u5247\u6211\u5011\u7528\u7684\u4e5f\u662f\u300c\u7406\u8ad6\u6982\u7387\u300d\u3002<\/span><\/li><\/ul><p>\u503c\u5f97\u7559\u610f\u7684\u662f\u53ea\u8981\u6211\u5011\u9032\u884c\u5927\u91cf\u8a66\u9a57\uff08\u4f8b\u5982\u64f2\u4e00\u842c\u6b21\u9280\u4ed4\uff09\uff0c\u300c\u5be6\u9a57\u6982\u7387\u300d\u61c9\u8207\u300c\u7406\u8ad6\u6982\u7387\u300d\u76f8\u7576\u63a5\u8fd1\u3002<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-bf670f0 elementor-widget elementor-widget-text-editor\" data-id=\"bf670f0\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<h3>11.5\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u671f\u671b\u51fa\u73fe\u7684\u6b21\u6578\u548c\u671f\u671b\u503c<\/h3><p>\u5047\u8a2d\u5728\u4e00\u6b21\u8a66\u9a57\u4e2d\uff08\u5982\u64f2\u9ab0\uff09\uff0c\u4e00\u4ef6\u4e8b\u4ef6\u767c\u751f\u7684\u6982\u7387\u662f p\u3002<br \/>\u5728\u7d93\u904e n \u6b21\u8a66\u9a57\u5f8c\uff0c\u8a72\u4e8b\u4ef6\u201c\u6703\u201d\u51fa\u73fe\u7684\u6b21\u6578 = np<\/p><p>\u6240\u8b02\u201c\u8a72\u4e8b\u4ef6\u6703\u51fa\u73fe\u7684\u6b21\u6578\u201d\u4fbf\u662f\u201c\u671f\u671b\u51fa\u73fe\u6b21\u6578\u201d\u4e86\u3002<\/p><p>\u4f8b3\uff1a\u3000 \u5c0f\u660e\u64f2\u9ab060\u6b21\uff0c\u6c42\u64f2\u5f971\u7684\u671f\u671b\u6b21\u6578\u3002<br \/>\u89e3\u8aaa\uff1a\u3000\u56e0\u70ba\u64f2\u5f97\u201c1\u201d\u7684\u6982\u7387\u662f1\/6\uff0c\u6240\u4ee5<br \/>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \\(\u64f2\u5f971\u7684\u671f\u671b\u6b21\u6578 = 60 \\times \\dfrac{1}{6} = 10\u6b21\\)<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-591021d elementor-widget elementor-widget-text-editor\" data-id=\"591021d\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<h3>11.6\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u671f\u671b\u503c<\/h3><p>\u300c\u671f\u671b\u503c\u300d\u5176\u5be6\u4fc2\u300c\u671f\u671b\u6b21\u6578\u300d\u7684\u5ef6\u4f38\u3002<\/p><p>\u4f8b4\uff1a\u3000\u5047\u5982\u55ba\u64f2\u9280\u4ed4\u904a\u6232\u4e2d\uff0c\u64f2\u5f97\u516c\u53ef\u5f97$5\uff0c\u64f2\u5f97\u5b57\u53ef\u5f97$1\u3002\u6c42\u64f2\u4e00\u6b21\u9280\u4ed4\u6642\u671f\u671b\u6240\u5f97\u7684\u91d1\u6214\u3002<br \/>\u89e3\u8aaa\uff1a\u3000\u7559\u610f\u55ba\u6982\u7387\u5165\u9762\uff0c\u671f\u671b\u503c\u4fc2\u201c\u5e73\u5747\u6211\u54cb\u6703\u651e\u5230\u5e7e\u591a\u201d\u3002<\/p><p style=\"padding-left: 40px;\">\u55ba\u4f9d\u500b\u4f8b\u5b50\u5165\u9762\uff0c\u56e0\u70ba\u67091\/2\u6a5f\u6703\u64f2\u516c\uff0c1\/2\u6a5f\u6703\u64f2\u5b57\uff0c\u6240\u4ee5\uff1a<\/p><p>\\(\u671f\u671b\u6240\u5f97\u7684\u91d1\u6214 = \\dfrac{1}{2} \\times $1+ \\dfrac{1}{2}\u00d7$5 = $3\\)<\/p><p>\u4f8b5\uff1a\u4e00\u500b\u888b\u5165\u9762\u670990\u500b\u767d\u6ce2\uff0c9\u500b\u9ed1\u6ce2\uff0c1\u500b\u7d05\u6ce2\u3002\u62bd\u5230\u767d\u6ce2\u5f971\u5206\u3001\u9ed1\u6ce25\u5206\u3001\u7d05\u6ce210\u5206\u3002\u6c42\u62bd\u6ce2\u4e00\u6b21\u6642\u5f97\u5206\u7684\u671f\u671b\u503c\u3002<br \/>\u89e3\u7b54\uff1a<br \/>\\(\\begin{align}<br \/>\u62bd\u6ce2\u4e00\u6b21\u6642\u5f97\u5206\u7684\u671f\u671b\u503c= \\dfrac{90}{100} \\times 1 + \\dfrac{9}{100} \\times 5 + \\dfrac{1}{100} \\times 10 \\\\ <br \/>= 1.45\u5206<br \/>\\end{align} \\)<\/p><p>\u5f9e\u4ee5\u4e0a\u5169\u500b\u4f8b\u5b50\uff0c\u5e0c\u671b\u5927\u5bb6\u660e\u767d\u5230\uff1a<\/p><p style=\"padding-left: 40px;\">\\(\u671f\u671b\u503c = P_{1} x_{1}+P_{2}x_{2}+\u22ef+P_{n} x_{n} \\)<\/p><p>\u7576\u4e2d<\/p><ul><li style=\"list-style-type: none;\"><ul><li>P<sub>1<\/sub>\u3001P<sub>2<\/sub>\u70ba\u4e8b\u4ef61\u3001\u4e8b\u4ef62\u767c\u751f\u7684\u6982\u7387\uff1b<\/li><li>x<sub>1<\/sub>\u3001x<sub>2<\/sub>\u70ba\u4e8b\u4ef61\u3001\u4e8b\u4ef62\u767c\u751f\u5f8c\u6240\u5f97\u7684\u503c<br \/>\uff08\u503c\u53ef\u4ee5\u4fc2\u201c\u5f97\u5206\u201d\uff0c\u201c\u596c\u91d1\u201d\u7b49\uff09<\/li><\/ul><\/li><\/ul>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-632f0da elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"632f0da\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-8f8e9ac\" data-id=\"8f8e9ac\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-810c117 elementor-widget elementor-widget-text-editor\" data-id=\"810c117\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form3_maths\/applications-of-trigonometry\/\"><i class=\"far fa-arrow-alt-circle-left\" aria-hidden=\"true\"><\/i> \u4e09\u89d2\u6bd4\u7684\u61c9\u7528<\/a>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-8e3907d\" data-id=\"8e3907d\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-52fdd5c\" data-id=\"52fdd5c\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-6f38e06 elementor-widget elementor-widget-text-editor\" data-id=\"6f38e06\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p style=\"text-align: right;\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form3_maths\/statistics-measure-of-central-tendency\/\">\u7d71\u8a08-\u96c6\u4e2d\u8da8\u52e2\u7684\u91cf\u5ea6 <i class=\"far fa-arrow-alt-circle-right\" aria-hidden=\"true\"><\/i><\/a><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-da52e11\" data-id=\"da52e11\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-a55f271 elementor-widget elementor-widget-sidebar\" data-id=\"a55f271\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"sidebar.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"sidebar-box widget-oceanwp-custom-menu custom-menu-widget clr\"><style type=\"text\/css\">.ocean_custom_menu-4 > ul > li > a, .custom-menu-widget .ocean_custom_menu-4 .dropdown-menu .sub-menu li a.menu-link{font-size:16px;line-height:17px;}.custom-menu-widget .ocean_custom_menu-4.oceanwp-custom-menu > ul.click-menu .open-this{font-size:16px;}<\/style><h4 class=\"widget-title\">\u4e2d\u4e09\u6578\u5b78\u3010\u76ee\u9304\u3011<\/h4><div class=\"oceanwp-custom-menu clr ocean_custom_menu-4 left dropdown-hover\"><ul id=\"menu-form3mathstopics\" class=\"dropdown-menu sf-menu\"><li  id=\"menu-item-1543\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1543\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form3_maths\/inequalities\/\" class=\"menu-link\">1. \u4e0d\u7b49\u5f0f (Inequalities)<\/a><\/li>\n<li  id=\"menu-item-1542\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1542\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form3_maths\/indices\/\" class=\"menu-link\">2. \u6307\u6578 (Indices)<\/a><\/li>\n<li  id=\"menu-item-1541\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1541\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form3_maths\/use-of-percentage\/\" class=\"menu-link\">3. \u767e\u4efd\u6cd5  (Use of Percentage)<\/a><\/li>\n<li  id=\"menu-item-1540\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1540\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form3_maths\/rational-irrational-numbers\/\" class=\"menu-link\">4. \u6709\u7406\u6578\u53ca\u7121\u7406\u6578 (Rational &#038; Irrational Numbers)<\/a><\/li>\n<li  id=\"menu-item-1539\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1539\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form3_maths\/deductive-geometry\/\" class=\"menu-link\">5. \u6f14\u7e79\u5e7e\u4f55 (Deductive Geometry)<\/a><\/li>\n<li  id=\"menu-item-1538\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1538\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form3_maths\/quadrilateral\/\" class=\"menu-link\">6. \u56db\u908a\u5f62 (Quadrilateral)<\/a><\/li>\n<li  id=\"menu-item-1537\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1537\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form3_maths\/area-volume\/\" class=\"menu-link\">7. \u9762\u7a4d\u8207\u9ad4\u7a4d (Area &#038; Volume)<\/a><\/li>\n<li  id=\"menu-item-1536\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1536\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form3_maths\/coordinate-geometry\/\" class=\"menu-link\">8. \u5750\u6a19\u5e7e\u4f55 (Coordinate Geometry)<\/a><\/li>\n<li  id=\"menu-item-1535\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1535\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form3_maths\/trigonometry\/\" class=\"menu-link\">9. \u4e09\u89d2\u5b78 (Trigonometry)<\/a><\/li>\n<li  id=\"menu-item-1534\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1534\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form3_maths\/applications-of-trigonometry\/\" class=\"menu-link\">10. \u4e09\u89d2\u6bd4\u7684\u61c9\u7528 (Applications of Trigonometry)<\/a><\/li>\n<li  id=\"menu-item-1533\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1533\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form3_maths\/probability\/\" class=\"menu-link\">11. \u6982\u7387 (Probability)<\/a><\/li>\n<li  id=\"menu-item-1532\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1532\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form3_maths\/statistics-measure-of-central-tendency\/\" class=\"menu-link\">12. \u7d71\u8a08 \u2013 \u96c6\u4e2d\u8da8\u52e2\u7684\u91cf\u5ea6 (Measure of Central Tendency)<\/a><\/li>\n<li  id=\"menu-item-1625\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1625\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form3_maths\/centers-of-triangles\/\" class=\"menu-link\">13. \u4e09\u89d2\u5f62\u7684\u5fc3 (Centers of Triangles)<\/a><\/li>\n<li  id=\"menu-item-16136\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-16136\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/exam_papers\/\" class=\"menu-link\">*** \u521d\u4e2d\u8a66\u5377 \/ \u8a66\u984c\u5eab ***<\/a><\/li>\n<\/ul><\/div><\/div>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>11.1\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u6982\u7387\u7684\u8a08\u7b97 \u6982\u7387\u662f\u7528\u4f86\u8868\u793a\u4e00\u4ef6\u4e8b\u4ef6\u767c\u751f\u7684\u53ef\u80fd\u6027\u3002\u8a2dE\u662f\u4e00\u4ef6\u4e8b\u4ef6\uff0c\u800cP(E)\u5247\u662f\u4e8b\u4ef6E [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":1463,"menu_order":10,"comment_status":"closed","ping_status":"closed","template":"elementor_header_footer","meta":{"ocean_post_layout":"","ocean_both_sidebars_style":"","ocean_both_sidebars_content_width":0,"ocean_both_sidebars_sidebars_width":0,"ocean_sidebar":"0","ocean_second_sidebar":"0","ocean_disable_margins":"enable","ocean_add_body_class":"","ocean_shortcode_before_top_bar":"","ocean_shortcode_after_top_bar":"","ocean_shortcode_before_header":"","ocean_shortcode_after_header":"","ocean_has_shortcode":"","ocean_shortcode_after_title":"","ocean_shortcode_before_footer_widgets":"","ocean_shortcode_after_footer_widgets":"","ocean_shortcode_before_footer_bottom":"","ocean_shortcode_after_footer_bottom":"","ocean_display_top_bar":"default","ocean_display_header":"default","ocean_header_style":"","ocean_center_header_left_menu":"0","ocean_custom_header_template":"0","ocean_custom_logo":0,"ocean_custom_retina_logo":0,"ocean_custom_logo_max_width":0,"ocean_custom_logo_tablet_max_width":0,"ocean_custom_logo_mobile_max_width":0,"ocean_custom_logo_max_height":0,"ocean_custom_logo_tablet_max_height":0,"ocean_custom_logo_mobile_max_height":0,"ocean_header_custom_menu":"0","ocean_menu_typo_font_family":"0","ocean_menu_typo_font_subset":"","ocean_menu_typo_font_size":0,"ocean_menu_typo_font_size_tablet":0,"ocean_menu_typo_font_size_mobile":0,"ocean_menu_typo_font_size_unit":"px","ocean_menu_typo_font_weight":"","ocean_menu_typo_font_weight_tablet":"","ocean_menu_typo_font_weight_mobile":"","ocean_menu_typo_transform":"","ocean_menu_typo_transform_tablet":"","ocean_menu_typo_transform_mobile":"","ocean_menu_typo_line_height":0,"ocean_menu_typo_line_height_tablet":0,"ocean_menu_typo_line_height_mobile":0,"ocean_menu_typo_line_height_unit":"","ocean_menu_typo_spacing":0,"ocean_menu_typo_spacing_tablet":0,"ocean_menu_typo_spacing_mobile":0,"ocean_menu_typo_spacing_unit":"","ocean_menu_link_color":"","ocean_menu_link_color_hover":"","ocean_menu_link_color_active":"","ocean_menu_link_background":"","ocean_menu_link_hover_background":"","ocean_menu_link_active_background":"","ocean_menu_social_links_bg":"","ocean_menu_social_hover_links_bg":"","ocean_menu_social_links_color":"","ocean_menu_social_hover_links_color":"","ocean_disable_title":"default","ocean_disable_heading":"default","ocean_post_title":"","ocean_post_subheading":"","ocean_post_title_style":"","ocean_post_title_background_color":"","ocean_post_title_background":0,"ocean_post_title_bg_image_position":"","ocean_post_title_bg_image_attachment":"","ocean_post_title_bg_image_repeat":"","ocean_post_title_bg_image_size":"","ocean_post_title_height":0,"ocean_post_title_bg_overlay":0.5,"ocean_post_title_bg_overlay_color":"","ocean_disable_breadcrumbs":"default","ocean_breadcrumbs_color":"","ocean_breadcrumbs_separator_color":"","ocean_breadcrumbs_links_color":"","ocean_breadcrumbs_links_hover_color":"","ocean_display_footer_widgets":"default","ocean_display_footer_bottom":"default","ocean_custom_footer_template":"0","footnotes":""},"class_list":["post-1501","page","type-page","status-publish","hentry","entry"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.9 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>11. \u6982\u7387 (Probability) &#187; \u9f4a\u9f4a\u6eab<\/title>\n<meta name=\"description\" content=\"\u6982\u7387\u662f\u7528\u4f86\u8868\u793a\u4e00\u4ef6\u4e8b\u4ef6\u767c\u751f\u7684\u53ef\u80fd\u6027\u3002\u8a2dE\u662f\u4e00\u4ef6\u4e8b\u4ef6\uff0c\u800cP(E)\u5247\u662f\u4e8b\u4ef6E\u767c\u751f\u7684\u6982\u7387\u3002\u9019\u57fa\u672c\u4e0a\u5c31\u662f\u6211\u5011\u5e73\u65e5\u6240\u8aaa\u7684\u300c\u6a5f\u6703\u7387\u300d\u3002\u4f8b\u5982\u64f2\u9280\u4ed4\u64f2\u5f97\u201c\u516c\u201d\u7684\u6a5f\u6703\u7387\uff08\u6982\u7387\uff09\u662f1\/2\u53ef\u4ee5\u5beb\u6210\uff1a P(\u64f2\u9280\u4ed4\u64f2\u5f97\u516c) = 1\/2\u3002\u55ba\u4f9d\u5ea6\uff0c\u6211\u5730\u6703\u6eab\u7fd2\u5413P(E) \u7684\u8a08\u7b97\u65b9\u6cd5\u3001\u6982\u7387\u7684\u6027\u8cea\u53ca\u89e3\u984c\u6280\u5de7\u3002\u5343\u5947\u5514\u597d\u932f\u904e!\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.study-together.com\/edu\/secondary\/form3_maths\/probability\/\" \/>\n<meta property=\"og:locale\" content=\"zh_TW\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"11. \u6982\u7387 (Probability) &#187; \u9f4a\u9f4a\u6eab\" \/>\n<meta property=\"og:description\" content=\"\u6982\u7387\u662f\u7528\u4f86\u8868\u793a\u4e00\u4ef6\u4e8b\u4ef6\u767c\u751f\u7684\u53ef\u80fd\u6027\u3002\u8a2dE\u662f\u4e00\u4ef6\u4e8b\u4ef6\uff0c\u800cP(E)\u5247\u662f\u4e8b\u4ef6E\u767c\u751f\u7684\u6982\u7387\u3002\u9019\u57fa\u672c\u4e0a\u5c31\u662f\u6211\u5011\u5e73\u65e5\u6240\u8aaa\u7684\u300c\u6a5f\u6703\u7387\u300d\u3002\u4f8b\u5982\u64f2\u9280\u4ed4\u64f2\u5f97\u201c\u516c\u201d\u7684\u6a5f\u6703\u7387\uff08\u6982\u7387\uff09\u662f1\/2\u53ef\u4ee5\u5beb\u6210\uff1a P(\u64f2\u9280\u4ed4\u64f2\u5f97\u516c) = 1\/2\u3002\u55ba\u4f9d\u5ea6\uff0c\u6211\u5730\u6703\u6eab\u7fd2\u5413P(E) \u7684\u8a08\u7b97\u65b9\u6cd5\u3001\u6982\u7387\u7684\u6027\u8cea\u53ca\u89e3\u984c\u6280\u5de7\u3002\u5343\u5947\u5514\u597d\u932f\u904e!\" \/>\n<meta property=\"og:url\" content=\"https:\/\/www.study-together.com\/edu\/secondary\/form3_maths\/probability\/\" \/>\n<meta property=\"og:site_name\" content=\"\u9f4a\u9f4a\u6eab\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/-100355795002387\" \/>\n<meta property=\"article:modified_time\" content=\"2020-11-02T15:19:51+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/www.study-together.com\/edu\/wp-content\/uploads\/2020\/07\/f3maths_probTreeDaig.jpg\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<script type=\"application\/ld+json\" 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