{"id":625,"date":"2025-12-09T16:07:48","date_gmt":"2025-12-09T08:07:48","guid":{"rendered":"https:\/\/book.yuekegu.com\/?p=625"},"modified":"2025-12-09T16:07:49","modified_gmt":"2025-12-09T08:07:49","slug":"11-1%e9%9a%8f%e6%9c%ba%e4%ba%8b%e4%bb%b6%e4%b8%8e%e6%a6%82%e7%8e%87","status":"publish","type":"post","link":"https:\/\/book.yuekegu.com\/index.php\/2025\/12\/09\/11-1%e9%9a%8f%e6%9c%ba%e4%ba%8b%e4%bb%b6%e4%b8%8e%e6%a6%82%e7%8e%87\/","title":{"rendered":"11.1\u968f\u673a\u4e8b\u4ef6\u4e0e\u6982\u7387"},"content":{"rendered":"\n<h1 class=\"wp-block-heading\">\u4e00\u3001\u57fa\u672c\u6982\u5ff5<\/h1>\n\n\n\n<p>\u6211\u4eec\u628a\u968f\u673a\u8bd5\u9a8c\u7684\u6bcf\u4e00\u4e2a\u53ef\u80fd\u7ed3\u679c\u79f0\u4e3a<strong>\u6837\u672c\u70b9<\/strong>(sample point)\uff0c\u7528$\\omega$\u8868\u793a\uff1b\u6240\u6709\u6837\u672c\u70b9\u7ec4\u6210\u7684\u96c6\u5408\u79f0\u4e3a<strong>\u6837\u672c\u7a7a\u95f4<\/strong>(sample space)\uff0c\u7528$\\Omega$\u8868\u793a\u3002\u5982\u679c\u6837\u672c\u7a7a\u95f4$\\Omega$\u662f\u4e00\u4e2a\u6709\u9650\u96c6\u5408\uff0c\u5219\u79f0\u6837\u672c\u7a7a\u95f4$\\Omega$\u4e3a<strong>\u6709\u9650\u6837\u672c\u7a7a\u95f4<\/strong>\u3002<\/p>\n\n\n\n<p>\u6837\u672c\u7a7a\u95f4\u7684\u5b50\u96c6\u79f0\u4e3a<strong>\u968f\u673a\u4e8b\u4ef6<\/strong>(random event)\uff0c\u7b80\u79f0<strong>\u4e8b\u4ef6<\/strong>\u3002\u4e8b\u4ef6\u4e00\u822c\u7528$A, B, C$\u7b49\u5927\u5199\u82f1\u6587\u5b57\u6bcd\u8868\u793a\u3002\u5f53\u4e00\u4e2a\u4e8b\u4ef6\u4ec5\u5305\u542b\u5355\u4e00\u6837\u672c\u70b9\u65f6\uff0c\u79f0\u8be5\u4e8b\u4ef6\u4e3a<strong>\u57fa\u672c\u4e8b\u4ef6<\/strong>(elementary event)\u3002<\/p>\n\n\n\n<p>\u663e\u7136\uff0c$\\Omega$\uff08\u5168\u96c6\uff09\u662f<strong>\u5fc5\u7136\u4e8b\u4ef6<\/strong>\uff0c$\\varnothing$\uff08\u7a7a\u96c6\uff09\u662f<strong>\u4e0d\u53ef\u80fd\u4e8b\u4ef6<\/strong>\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u76f8\u5173\u95ee\u9898<\/h3>\n\n\n\n<p>\u82e5\u968f\u673a\u8bd5\u9a8c\u7684\u6837\u672c\u7a7a\u95f4\u662f$\\Omega$\uff0c\u4e14$A$\u662f\u4e00\u4e2a\u5fc5\u7136\u4e8b\u4ef6\uff0c$B$\u662f\u4e00\u4e2a\u4e0d\u53ef\u80fd\u4e8b\u4ef6\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u5199\u51fa$A$\u4e0e$\\Omega$\u7684\u5173\u7cfb\uff1b<\/li>\n\n\n\n<li>\u5199\u51fa$B$\u4e0e$\\varnothing$\u7684\u5173\u7cfb\u3002<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading\">\u4f8b\u9898\uff08\u4f8b4\uff09<\/h3>\n\n\n\n<p>\u5148\u540e\u4e24\u6b21\u63b7\u4e00\u4e2a\u5747\u5300\u7684\u9ab0\u5b50\uff0c\u89c2\u5bdf\u671d\u4e0a\u7684\u9762\u7684\u70b9\u6570\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u5199\u51fa\u5bf9\u5e94\u7684\u6837\u672c\u7a7a\u95f4<\/strong><br>\u56e0\u6b64\uff0c\u6837\u672c\u7a7a\u95f4<br>$$\\Omega={(i, j) | 1 \\leq i \\leq 6, 1 \\leq j \\leq 6, i \\in N, j \\in N}$$<\/li>\n\n\n\n<li><strong>\u7528\u96c6\u5408\u8868\u793a\u4e8b\u4ef6<\/strong>\n<ul class=\"wp-block-list\">\n<li>\u4e8b\u4ef6$A$\uff1a\u70b9\u6570\u4e4b\u548c\u4e3a3<br>$$A={(1,2),(2,1)}$$<\/li>\n\n\n\n<li>\u4e8b\u4ef6$B$\uff1a\u70b9\u6570\u4e4b\u548c\u4e0d\u8d85\u8fc73<br>$$B={(1,1),(1,2),(2,1)}$$<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>\u5224\u65ad$P(A)$\u548c$P(B)$\u7684\u5927\u5c0f<\/strong><br>\u56e0\u4e3a$A$\u4e8b\u4ef6\u53d1\u751f\u65f6\uff0c$B$\u4e8b\u4ef6\u4e00\u5b9a\u53d1\u751f\uff0c\u4e5f\u5c31\u662f\u8bf4$B$\u4e8b\u4ef6\u53d1\u751f\u7684\u53ef\u80fd\u6027\u4e0d\u4f1a\u6bd4$A$\u4e8b\u4ef6\u53d1\u751f\u7684\u53ef\u80fd\u6027\u5c0f\uff0c\u6240\u4ee5\u76f4\u89c2\u4e0a\u53ef\u77e5$P(A) \\leq P(B)$\u3002<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading\">\u62d3\u5c55\u7ec3\u4e60<\/h3>\n\n\n\n<p>\u6309\u5148\u540e\u987a\u5e8f\u629b\u4e09\u679a\u786c\u5e01\uff0c\u89c2\u5bdf\u6b63\u53cd\u9762\u51fa\u73b0\u7684\u60c5\u51b5\uff0c\u9009\u62e9\u5408\u9002\u7684\u65b9\u6cd5\u8868\u793a\u6837\u672c\u70b9\uff0c\u5e76\u5199\u51fa\u6837\u672c\u7a7a\u95f4\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u4e8c\u3001\u4e8b\u4ef6\u4e4b\u95f4\u7684\u5173\u7cfb\u548c\u8fd0\u7b97<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">1. \u4e8b\u4ef6\u5173\u7cfb\u4e0e\u8fd0\u7b97\u7684\u57fa\u672c\u7c7b\u578b<\/h3>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>\u4e8b\u4ef6\u7684\u5173\u7cfb\u6216\u8fd0\u7b97<\/th><th>\u542b\u4e49<\/th><th>\u7b26\u53f7\u8868\u793a<\/th><\/tr><\/thead><tbody><tr><td>\u5305\u542b<\/td><td>$A$\u53d1\u751f\u5bfc\u81f4$B$\u53d1\u751f<\/td><td>$A\\subset B$<\/td><\/tr><tr><td>\u5e76\u4e8b\u4ef6\uff08\u548c\u4e8b\u4ef6\uff09<\/td><td>$A$\u4e0e$B$\u81f3\u5c11\u4e00\u4e2a\u53d1\u751f<\/td><td>$A\\cup B$\u6216$A+B$<\/td><\/tr><tr><td>\u4ea4\u4e8b\u4ef6\uff08\u79ef\u4e8b\u4ef6\uff09<\/td><td>$A$\u4e0e$B$\u540c\u65f6\u53d1\u751f<\/td><td>$A\\cap B$\u6216$AB$<\/td><\/tr><tr><td>\u4e92\u65a5\uff08\u4e92\u4e0d\u76f8\u5bb9\uff09<\/td><td>$A$\u4e0e$B$\u4e0d\u80fd\u540c\u65f6\u53d1\u751f<\/td><td>$A\\cap B=\\varnothing$<\/td><\/tr><tr><td>\u4e92\u4e3a\u5bf9\u7acb<\/td><td>$A$\u4e0e$B$\u6709\u4e14\u4ec5\u6709\u4e00\u4e2a\u53d1\u751f<\/td><td>$A\\cap B=\\varnothing$\uff0c$A\\cup B=\\Omega$<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\">2. \u591a\u4e2a\u4e8b\u4ef6\u7684\u62d3\u5c55<\/h3>\n\n\n\n<p>\u7c7b\u4f3c\u5730\uff0c\u6211\u4eec\u53ef\u4ee5\u5b9a\u4e49\u591a\u4e2a\u4e8b\u4ef6\u7684\u548c\u4e8b\u4ef6\u4ee5\u53ca\u79ef\u4e8b\u4ef6\u3002\u4f8b\u5982\uff0c\u5bf9\u4e8e\u4e09\u4e2a\u4e8b\u4ef6$A, B, C$\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>$A \\cup B \\cup C$\uff08\u6216$A+B+C$\uff09\u53d1\u751f\u5f53\u4e14\u4ec5\u5f53$A, B, C$\u4e2d\u81f3\u5c11\u4e00\u4e2a\u53d1\u751f\uff1b<\/li>\n\n\n\n<li>$A \\cap B \\cap C$\uff08\u6216$ABC$\uff09\u53d1\u751f\u5f53\u4e14\u4ec5\u5f53$A, B, C$\u540c\u65f6\u53d1\u751f\u3002<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">3. \u4e8b\u4ef6\u8868\u8fbe\u5f0f\u542b\u4e49\u5206\u6790<\/h3>\n\n\n\n<p>\u8bbe$A, B, C$\u4e3a\u4e09\u4e2a\u4e8b\u4ef6\uff0c\u8bf4\u660e\u4e0b\u5217\u5404\u5f0f\u6240\u8868\u793a\u7684\u610f\u4e49\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>$\\overline{A} B C$\uff1b<\/li>\n\n\n\n<li>$\\overline{A+B+C}$\uff1b<\/li>\n\n\n\n<li>$ABC+\\overline{A}BC+A\\overline{B}C+AB\\overline{C}$\uff08\u6ce8\uff1a\u539f\u6587\u8868\u8fbe\u5f0f\u5b58\u5728\u91cd\u590d\uff0c\u6b64\u5904\u4fee\u6b63\u4e3a\u5e38\u89c1\u5f62\u5f0f\uff09\u3002<\/li>\n<\/ol>\n\n\n\n<h2 class=\"wp-block-heading\">\u4e09\u3001\u53e4\u5178\u6982\u578b<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">1. \u53e4\u5178\u6982\u578b\u7684\u7279\u5f81<\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u6709\u9650\u6027<\/strong>\uff1a\u6837\u672c\u7a7a\u95f4\u7684\u6837\u672c\u70b9\u53ea\u6709\u6709\u9650\u4e2a\uff1b<\/li>\n\n\n\n<li><strong>\u7b49\u53ef\u80fd\u6027<\/strong>\uff1a\u6bcf\u4e2a\u6837\u672c\u70b9\u53d1\u751f\u7684\u53ef\u80fd\u6027\u76f8\u7b49\u3002<\/li>\n<\/ol>\n\n\n\n<p>\u6211\u4eec\u5c06\u5177\u6709\u4ee5\u4e0a\u4e24\u4e2a\u7279\u5f81\u7684\u8bd5\u9a8c\u79f0\u4e3a<strong>\u53e4\u5178\u6982\u578b\u8bd5\u9a8c<\/strong>\uff0c\u5176\u6570\u5b66\u6a21\u578b\u79f0\u4e3a<strong>\u53e4\u5178\u6982\u7387\u6a21\u578b<\/strong>\uff0c\u7b80\u79f0<strong>\u53e4\u5178\u6982\u578b<\/strong>\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">2. \u4f8b\u9898\uff08\u4f8b8\uff09<\/h3>\n\n\n\n<p>\u629b\u63b7\u4e24\u679a\u8d28\u5730\u5747\u5300\u7684\u9ab0\u5b50\uff08\u6807\u8bb0\u4e3aI\u53f7\u548cII\u53f7\uff09\uff0c\u89c2\u5bdf\u4e24\u9ab0\u5b50\u5206\u522b\u53ef\u80fd\u51fa\u73b0\u7684\u57fa\u672c\u7ed3\u679c\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u5199\u51fa\u6837\u672c\u7a7a\u95f4\u5e76\u5224\u65ad\u662f\u5426\u4e3a\u53e4\u5178\u6982\u578b<\/strong>\uff1b<\/li>\n\n\n\n<li><strong>\u6c42\u4e0b\u5217\u4e8b\u4ef6\u7684\u6982\u7387<\/strong>\n<ul class=\"wp-block-list\">\n<li>$A=$&#8221;\u4e24\u4e2a\u70b9\u6570\u4e4b\u548c\u662f5&#8243;\uff1b<\/li>\n\n\n\n<li>$B=$&#8221;\u4e24\u4e2a\u70b9\u6570\u76f8\u7b49&#8221;\uff1b<\/li>\n\n\n\n<li>$C=$&#8221;I\u53f7\u9ab0\u5b50\u7684\u70b9\u6570\u5927\u4e8eII\u53f7\u9ab0\u5b50\u7684\u70b9\u6570&#8221;\u3002<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading\">3. \u601d\u8003\u95ee\u9898<\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u5728\u4f8b8\u4e2d\uff0c\u4e3a\u4ec0\u4e48\u8981\u628a\u4e24\u679a\u9ab0\u5b50\u6807\u4e0a\u8bb0\u53f7\uff1f\u5982\u679c\u4e0d\u7ed9\u4e24\u679a\u9ab0\u5b50\u6807\u8bb0\u53f7\uff0c\u4f1a\u51fa\u73b0\u4ec0\u4e48\u60c5\u51b5\uff1f\u4f60\u80fd\u89e3\u91ca\u5176\u4e2d\u7684\u539f\u56e0\u5417\uff1f\n<ul class=\"wp-block-list\">\n<li>\u5f53\u4e0d\u7ed9\u4e24\u679a\u9ab0\u5b50\u6807\u8bb0\u53f7\u65f6\uff0c\u8bd5\u9a8c\u7684\u6837\u672c\u7a7a\u95f4$\\Omega_{1}={(m, n) | m,n \\in{1,2,3,4,5,6},\u4e14 m \\leq n}$\uff0c\u5219$n(\\Omega_{1})=21$\u3002\u5176\u4e2d\uff0c\u4e8b\u4ef6$A=$&#8221;\u4e24\u4e2a\u70b9\u6570\u4e4b\u548c\u662f5&#8243;\u7684\u7ed3\u679c\u53d8\u4e3a$A={(1,4),(2,3)}$\uff0c\u8fd9\u65f6$P(A)=\\frac{2}{21}$\u3002<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>\u540c\u4e00\u4e2a\u4e8b\u4ef6\u7684\u6982\u7387\uff0c\u4e3a\u4ec0\u4e48\u4f1a\u51fa\u73b0\u4e24\u4e2a\u4e0d\u540c\u7684\u7ed3\u679c\u5462\uff1f<\/li>\n<\/ol>\n\n\n\n<h2 class=\"wp-block-heading\">\u56db\u3001\u63a2\u7a76\u00b7\u62d3\u5c55\u9898\u578b<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">1. \u9f50\u738b\u4e0e\u7530\u5fcc\u8d5b\u9a6c\u95ee\u9898<\/h3>\n\n\n\n<p>\u7530\u5fcc\u7684\u4e0a\u7b49\u9a6c\u4f18\u4e8e\u9f50\u738b\u7684\u4e2d\u7b49\u9a6c\uff0c\u52a3\u4e8e\u9f50\u738b\u7684\u4e0a\u7b49\u9a6c\uff1b\u7530\u5fcc\u7684\u4e2d\u7b49\u9a6c\u4f18\u4e8e\u9f50\u738b\u7684\u4e0b\u7b49\u9a6c\uff0c\u52a3\u4e8e\u9f50\u738b\u7684\u4e2d\u7b49\u9a6c\uff1b\u7530\u5fcc\u7684\u4e0b\u7b49\u9a6c\u52a3\u4e8e\u9f50\u738b\u7684\u4e0b\u7b49\u9a6c\u3002\u73b0\u53cc\u65b9\u5404\u51fa\u4e0a\u3001\u4e2d\u3001\u4e0b\u7b49\u9a6c\u54041\u5339\u5206\u7ec4\u5206\u522b\u8fdb\u884c1\u573a\u6bd4\u8d5b\uff0c\u80dc2\u573a\u53ca\u4ee5\u4e0a\u8005\u83b7\u80dc\u3002\u82e5\u53cc\u65b9\u5747\u4e0d\u77e5\u5bf9\u65b9\u9a6c\u7684\u51fa\u573a\u987a\u5e8f\uff0c\u8bd5\u6c42\u7530\u5fcc\u83b7\u80dc\u7684\u6982\u7387\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">2. 2024\u65b0\u9ad8\u8003\u2160\u5377\u00b714<\/h3>\n\n\n\n<p>\u7532\u3001\u4e59\u4e24\u4eba\u5404\u6709\u56db\u5f20\u5361\u7247\uff0c\u6bcf\u5f20\u5361\u7247\u4e0a\u6807\u6709\u4e00\u4e2a\u6570\u5b57\uff0c\u7532\u7684\u5361\u7247\u4e0a\u5206\u522b\u6807\u6709\u6570\u5b571,3,5,7\uff0c\u4e59\u7684\u5361\u7247\u4e0a\u5206\u522b\u6807\u6709\u6570\u5b572,4,6,8\uff0c\u4e24\u4eba\u8fdb\u884c\u56db\u8f6e\u6bd4\u8d5b\uff0c\u5728\u6bcf\u8f6e\u6bd4\u8d5b\u4e2d\uff0c\u4e24\u4eba\u5404\u81ea\u4ece\u81ea\u5df1\u6301\u6709\u7684\u5361\u7247\u4e2d\u968f\u673a\u9009\u4e00\u5f20\uff0c\u5e76\u6bd4\u8f83\u6240\u9009\u5361\u7247\u4e0a\u6570\u5b57\u7684\u5927\u5c0f\uff0c\u6570\u5b57\u5927\u7684\u4eba\u5f971\u5206\uff0c\u6570\u5b57\u5c0f\u7684\u4eba\u5f970\u5206\uff0c\u7136\u540e\u5404\u81ea\u5f03\u7f6e\u6b64\u8f6e\u6240\u9009\u7684\u5361\u7247\uff08\u5f03\u7f6e\u7684\u5361\u7247\u5728\u6b64\u540e\u7684\u8f6e\u6b21\u4e2d\u4e0d\u80fd\u4f7f\u7528\uff09\u3002\u5219\u56db\u8f6e\u6bd4\u8d5b\u540e\uff0c\u7532\u7684\u603b\u5f97\u5206\u4e0d\u5c0f\u4e8e2\u7684\u6982\u7387\u4e3a<strong>__<\/strong>\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">3. 2024\u00b7\u5168\u56fd\u7532\u5377<\/h3>\n\n\n\n<p>\u67096\u4e2a\u76f8\u540c\u7684\u7403\uff0c\u5206\u522b\u6807\u6709\u6570\u5b571\u30012\u30013\u30014\u30015\u30016\uff0c\u4ece\u4e2d\u65e0\u653e\u56de\u5730\u968f\u673a\u53d63\u6b21\uff0c\u6bcf\u6b21\u53d61\u4e2a\u7403\u3002\u8bb0$m$\u4e3a\u524d\u4e24\u6b21\u53d6\u51fa\u7684\u7403\u4e0a\u6570\u5b57\u7684\u5e73\u5747\u503c\uff0c$n$\u4e3a\u53d6\u51fa\u7684\u4e09\u4e2a\u7403\u4e0a\u6570\u5b57\u7684\u5e73\u5747\u503c\uff0c\u5219$m$\u4e0e$n$\u4e4b\u5dee\u7684\u7edd\u5bf9\u503c\u4e0d\u5927\u4e8e$\\frac{1}{2}$\u7684\u6982\u7387\u4e3a<strong>__<\/strong>\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">4. 2022\u00b7\u5168\u56fd\u7532\u5377<\/h3>\n\n\n\n<p>\u4ece\u6b63\u65b9\u4f53\u76848\u4e2a\u9876\u70b9\u4e2d\u4efb\u90094\u4e2a\uff0c\u5219\u8fd94\u4e2a\u70b9\u5728\u540c\u4e00\u4e2a\u5e73\u9762\u7684\u6982\u7387\u4e3a$\\boxed{\\frac{6}{35}}$\u3002<br><strong>\u89e3\u6790<\/strong>\uff1a\u4ece\u6b63\u65b9\u4f53\u76848\u4e2a\u9876\u70b9\u4e2d\u4efb\u90094\u4e2a\uff0c\u53d6\u6cd5\u6709$C_{8}^{4}=70$\uff08\u79cd\uff09\u3002\u5176\u4e2d4\u4e2a\u70b9\u5171\u9762\u6709\u4ee5\u4e0b\u4e24\u79cd\u60c5\u51b5\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u6240\u53d6\u76844\u4e2a\u70b9\u4e3a\u6b63\u65b9\u4f53\u540c\u4e00\u4e2a\u9762\u4e0a\u76844\u4e2a\u9876\u70b9\uff0c\u67096\u79cd\u53d6\u6cd5\uff1b<\/li>\n\n\n\n<li>\u6240\u53d6\u76844\u4e2a\u70b9\u4e3a\u6b63\u65b9\u4f53\u540c\u4e00\u4e2a\u5bf9\u89d2\u9762\u4e0a\u76844\u4e2a\u9876\u70b9\uff0c\u4e5f\u67096\u79cd\u53d6\u6cd5\u3002<\/li>\n<\/ol>\n\n\n\n<p>\u6240\u4ee5\u6240\u53d6\u76844\u4e2a\u70b9\u5728\u540c\u4e00\u4e2a\u5e73\u9762\u7684\u6982\u7387$P=\\frac{12}{70}=\\frac{6}{35}$\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u4e94\u3001\u6982\u7387\u7684\u6027\u8d28<\/h2>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u5bf9\u4efb\u610f\u7684\u4e8b\u4ef6$A$\uff0c\u90fd\u6709$P(A) \\geq 0$\uff1b<\/li>\n\n\n\n<li>$P(\\Omega)=\\boxed{1}$\uff0c$P(\\varnothing)=\\boxed{0}$\uff1b<\/li>\n\n\n\n<li>\u5982\u679c\u4e8b\u4ef6$A$\u4e0e\u4e8b\u4ef6$B$\u4e92\u65a5\uff0c\u90a3\u4e48$P(A\\cup B)=\\boxed{P(A)+P(B)}$\uff1b<\/li>\n\n\n\n<li>\u5982\u679c\u4e8b\u4ef6$A$\u4e0e\u4e8b\u4ef6$B$\u4e92\u4e3a\u5bf9\u7acb\u4e8b\u4ef6\uff0c\u90a3\u4e48$P(B)=\\boxed{1-P(A)}$\uff0c$P(A)=\\boxed{1-P(B)}$\uff1b<\/li>\n\n\n\n<li>\u56e0\u4e3a$\\varnothing \\subseteq A \\subseteq \\Omega$\uff0c\u6240\u4ee5$0 \\leq P(A) \\leq 1$\uff1b\u5982\u679c$A\\subseteq B$\uff0c\u90a3\u4e48$P(A)\\boxed{\\leq}P(B)$\uff1b<\/li>\n\n\n\n<li>\u8bbe$A,B$\u662f\u4e00\u4e2a\u968f\u673a\u8bd5\u9a8c\u4e2d\u7684\u4e24\u4e2a\u4e8b\u4ef6\uff0c\u6709$P(A\\cup B)=\\boxed{P(A)+P(B)-P(A\\cap B)}$\u3002<\/li>\n<\/ol>\n\n\n\n<h2 class=\"wp-block-heading\">\u516d\u3001\u4f5c\u4e1a\u4e0e\u7ec3\u4e60<\/h2>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u5b8c\u6210\u84dd\u76ae\u5269\u4e0b\u7684\u4f8b\u9898\u53ca\u53d8\u5f0f\uff1b<\/li>\n\n\n\n<li>\u5b8c\u6210\u5468\u672b\u7ec3\u4e60\u3002<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"<p>\u4e00\u3001\u57fa\u672c\u6982\u5ff5 \u6211\u4eec\u628a\u968f\u673a\u8bd5\u9a8c\u7684\u6bcf\u4e00\u4e2a\u53ef\u80fd\u7ed3\u679c\u79f0\u4e3a\u6837\u672c\u70b9(sample point)\uff0c\u7528$\\omega$\u8868\u793a\uff1b\u6240\u6709\u6837\u672c\u70b9\u7ec4\u6210\u7684\u96c6\u5408\u79f0\u4e3a\u6837\u672c\u7a7a\u95f4(sample space)\uff0c\u7528$\\Omega$\u8868\u793a\u3002\u5982\u679c\u6837\u672c\u7a7a\u95f4$\\Omega$\u662f\u4e00\u4e2a\u6709\u9650\u96c6\u5408\uff0c\u5219\u79f0\u6837\u672c\u7a7a\u95f4$\\Omega$\u4e3a\u6709\u9650\u6837\u672c\u7a7a\u95f4\u3002 \u6837\u672c\u7a7a\u95f4\u7684\u5b50\u96c6\u79f0\u4e3a\u968f\u673a\u4e8b\u4ef6(random event)\uff0c\u7b80\u79f0\u4e8b\u4ef6\u3002\u4e8b\u4ef6\u4e00\u822c\u7528$A, B, C$\u7b49\u5927\u5199\u82f1\u6587\u5b57\u6bcd\u8868\u793a\u3002\u5f53\u4e00\u4e2a\u4e8b\u4ef6\u4ec5\u5305\u542b\u5355\u4e00\u6837\u672c\u70b9\u65f6\uff0c\u79f0\u8be5\u4e8b\u4ef6\u4e3a\u57fa\u672c\u4e8b\u4ef6(elementary event)\u3002 \u663e\u7136\uff0c$\\Omega$\uff08\u5168\u96c6\uff09\u662f\u5fc5\u7136\u4e8b\u4ef6\uff0c$\\varnothing$\uff08\u7a7a\u96c6\uff09\u662f\u4e0d\u53ef\u80fd\u4e8b\u4ef6\u3002 \u76f8\u5173\u95ee\u9898 \u82e5\u968f\u673a\u8bd5\u9a8c\u7684\u6837\u672c\u7a7a\u95f4\u662f$\\Omega$\uff0c\u4e14$A$\u662f\u4e00\u4e2a\u5fc5\u7136\u4e8b\u4ef6\uff0c$B$\u662f\u4e00\u4e2a\u4e0d\u53ef\u80fd\u4e8b\u4ef6\uff1a \u4f8b\u9898\uff08\u4f8b4\uff09 \u5148\u540e\u4e24\u6b21\u63b7\u4e00\u4e2a\u5747\u5300\u7684\u9ab0\u5b50\uff0c\u89c2\u5bdf\u671d\u4e0a\u7684\u9762\u7684\u70b9\u6570\uff1a \u62d3\u5c55\u7ec3\u4e60 \u6309\u5148\u540e\u987a\u5e8f\u629b\u4e09\u679a\u786c\u5e01\uff0c\u89c2\u5bdf\u6b63\u53cd\u9762\u51fa\u73b0\u7684\u60c5\u51b5\uff0c\u9009\u62e9\u5408\u9002\u7684\u65b9\u6cd5\u8868\u793a\u6837\u672c\u70b9\uff0c\u5e76\u5199\u51fa\u6837\u672c\u7a7a\u95f4\u3002 \u4e8c\u3001\u4e8b\u4ef6\u4e4b\u95f4\u7684\u5173\u7cfb\u548c\u8fd0\u7b97 1. \u4e8b\u4ef6\u5173\u7cfb\u4e0e\u8fd0\u7b97\u7684\u57fa\u672c\u7c7b\u578b \u4e8b\u4ef6\u7684\u5173\u7cfb\u6216\u8fd0\u7b97 \u542b\u4e49 \u7b26\u53f7\u8868\u793a \u5305\u542b $A$\u53d1\u751f\u5bfc\u81f4$B$\u53d1\u751f $A\\subset B$ \u5e76\u4e8b\u4ef6\uff08\u548c\u4e8b\u4ef6\uff09 $A$\u4e0e$B$\u81f3\u5c11\u4e00\u4e2a\u53d1\u751f $A\\cup B$\u6216$A+B$ \u4ea4\u4e8b\u4ef6\uff08\u79ef\u4e8b\u4ef6\uff09 $A$\u4e0e$B$\u540c\u65f6\u53d1\u751f $A\\cap B$\u6216$AB$ \u4e92\u65a5\uff08\u4e92\u4e0d\u76f8\u5bb9\uff09 $A$\u4e0e$B$\u4e0d\u80fd\u540c\u65f6\u53d1\u751f $A\\cap B=\\varnothing$ \u4e92\u4e3a\u5bf9\u7acb $A$\u4e0e$B$\u6709\u4e14\u4ec5\u6709\u4e00\u4e2a\u53d1\u751f $A\\cap B=\\varnothing$\uff0c$A\\cup [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[44,45],"tags":[],"class_list":["post-625","post","type-post","status-publish","format-standard","hentry","category-44","category-45"],"_links":{"self":[{"href":"https:\/\/book.yuekegu.com\/index.php\/wp-json\/wp\/v2\/posts\/625","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/book.yuekegu.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/book.yuekegu.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/book.yuekegu.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/book.yuekegu.com\/index.php\/wp-json\/wp\/v2\/comments?post=625"}],"version-history":[{"count":1,"href":"https:\/\/book.yuekegu.com\/index.php\/wp-json\/wp\/v2\/posts\/625\/revisions"}],"predecessor-version":[{"id":626,"href":"https:\/\/book.yuekegu.com\/index.php\/wp-json\/wp\/v2\/posts\/625\/revisions\/626"}],"wp:attachment":[{"href":"https:\/\/book.yuekegu.com\/index.php\/wp-json\/wp\/v2\/media?parent=625"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/book.yuekegu.com\/index.php\/wp-json\/wp\/v2\/categories?post=625"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/book.yuekegu.com\/index.php\/wp-json\/wp\/v2\/tags?post=625"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}