{"id":2125,"date":"2023-04-02T09:46:24","date_gmt":"2023-04-02T01:46:24","guid":{"rendered":"https:\/\/www.appblog.cn\/?p=2125"},"modified":"2023-04-05T20:42:06","modified_gmt":"2023-04-05T12:42:06","slug":"fundamentals-of-high-school-mathematics-probability-and-statistics","status":"publish","type":"post","link":"https:\/\/www.appblog.cn\/index.php\/2023\/04\/02\/fundamentals-of-high-school-mathematics-probability-and-statistics\/","title":{"rendered":"\u9ad8\u4e2d\u6570\u5b66\u57fa\u7840\uff1a\u6982\u7387\u4e0e\u7edf\u8ba1"},"content":{"rendered":"<h2>\u57fa\u672c\u6982\u5ff5<\/h2>\n<p>\u51fd\u6570\u5173\u7cfb\u662f\u4e00\u79cd\u786e\u5b9a\u6027\u5173\u7cfb\uff0c\u76f8\u5173\u5173\u7cfb\u662f\u4e00\u79cd\u975e\u786e\u5b9a\u6027\u5173\u7cfb<br \/>\n\u5224\u65ad\u4e24\u4e2a\u53d8\u91cf\u95f4\u7684\u5173\u7cfb\u662f\u5426\u4e3a\u76f8\u5173\u5173\u7cfb\u7684\u5173\u952e\u662f\u770b\u8fd9\u4e2a\u5173\u7cfb\u662f\u5426\u5177\u6709\u4e0d\u786e\u5b9a\u6027<\/p>\n<p><!-- more --><\/p>\n<p>\u6982\u7387\u662f\u4e00\u4e2a\u7a33\u5b9a\u7684\u6570\u503c\uff0c\u4e5f\u5c31\u662f\u67d0\u4ef6\u4e8b\u53d1\u751f\u6216\u4e0d\u53d1\u751f\u7684\u6982\u7387\u662f\u591a\u5c11<br \/>\n\u9891\u7387\u662f\u5728\u4e00\u5b9a\u6570\u91cf\u7684\u67d0\u4ef6\u4e8b\u60c5\u4e0a\u9762\uff0c\u53d1\u751f\u7684\u6570\u4e0e\u603b\u6570\u7684\u6bd4\u503c.<br \/>\n\u5047\u8bbe\u4e8b\u4ef6$A$\u7684\u6982\u7387\u662f0.3\uff0c\u5728100\u6b21\u4e2d\u53d1\u751f28\u6b21\uff0c\u90a3\u4e48\u5b83\u7684\u9891\u7387\u662f28\/100=0.28<br \/>\n\u9891\u7387\u662f\u6709\u9650\u6b21\u6570\u7684\u8bd5\u9a8c\u6240\u5f97\u7684\u7ed3\u679c\uff0c\u6982\u7387\u662f\u9891\u6570\u65e0\u9650\u5927\u65f6\u5bf9\u5e94\u7684\u9891\u7387<\/p>\n<p>\u9891\u7387\u7684\u7a33\u5b9a\u503c\u662f\u6982\u7387\uff0c\u9891\u7387\u968f\u8bd5\u9a8c\u6b21\u6570\u7684\u4e0d\u540c\u662f\u53d8\u5316\u7684\uff0c\u662f\u4e00\u4e2a\u7edf\u8ba1\u89c4\u5f8b\uff0c\u4f46\u5b83\u90fd\u5728\u6982\u7387\u9644\u8fd1\u6446\u52a8\uff0c\u800c\u4e00\u4e2a\u4e8b\u4ef6\u7684\u6982\u7387\u662f\u4e0d\u53d8\u7684<\/p>\n<h2>\u62bd\u6837\u65b9\u6cd5<\/h2>\n<p>\u2460 \u7b80\u5355\u968f\u673a\u62bd\u6837\uff08\u603b\u4f53\u4e2a\u6570\u8f83\u5c11\uff09<br \/>\n\u2461 \u7cfb\u7edf\u62bd\u6837\uff08\u603b\u4f53\u4e2a\u6570\u8f83\u591a\uff09<br \/>\n\u2462 \u5206\u5c42\u62bd\u6837\uff08\u603b\u4f53\u4e2d\u5dee\u5f02\u660e\u663e\uff09<\/p>\n<p>\u6ce8\u610f\uff1a\u5728$N$\u4e2a\u4e2a\u4f53\u7684\u603b\u4f53\u4e2d\u62bd\u53d6\u51fa$n$\u4e2a\u4e2a\u4f53\u7ec4\u6210\u6837\u672c\uff0c\u6bcf\u4e2a\u4e2a\u4f53\u88ab\u62bd\u5230\u7684\u673a\u4f1a\uff08\u6982\u7387\uff09\u5747\u4e3a$\\frac{n}{N}$<\/p>\n<h2>\u603b\u4f53\u7279\u5f81\u6570\u7684\u4f30\u8ba1<\/h2>\n<p>\uff081\uff09\u5e73\u5747\u6570<\/p>\n<p>$$<br \/>\n\\overline{x} = \\frac{x_1+x_2+x_3+\u00b7\u00b7\u00b7+x_n}{n}<br \/>\n$$<\/p>\n<p>\u53d6\u503c\u4e3a$x_1,x_2,\u00b7\u00b7\u00b7,x_n$\u7684\u9891\u7387\u5206\u522b\u4e3a$p_1,p_2,\u00b7\u00b7\u00b7,p_n$\uff0c\u5219\u5176\u5e73\u5747\u6570\u4e3a$x_1p_1,x_2p_2,\u00b7\u00b7\u00b7,x_np_n$<\/p>\n<p>\uff082\uff09\u65b9\u5dee<\/p>\n<p>$$<br \/>\ns^2 = \\frac{1}{n}\\sum_{i=1}^n(x_i-\\overline{x})^2<br \/>\n$$<\/p>\n<p>\uff083\uff09\u6807\u51c6\u5dee<\/p>\n<p>$$<br \/>\ns = \\sqrt{\\frac{1}{n}\\sum_{i=1}^n(x_i-\\overline{x})^2}<br \/>\n$$<\/p>\n<blockquote>\n<p>\u6ce8\uff1a\u65b9\u5dee\u4e0e\u6807\u51c6\u5dee\u8d8a\u5c0f\uff0c\u8bf4\u660e\u6837\u672c\u6570\u636e\u8d8a\u7a33\u5b9a\u3002\u5e73\u5747\u6570\u53cd\u6620\u6570\u636e\u603b\u4f53\u6c34\u5e73\uff0c\u65b9\u5dee\u4e0e\u6807\u51c6\u5dee\u53cd\u6620\u6570\u636e\u7684\u7a33\u5b9a\u6c34\u5e73\u3002<\/p>\n<\/blockquote>\n<h2>\u7ebf\u6027\u56de\u5f52\u65b9\u7a0b<\/h2>\n<p>\u2460 \u53d8\u91cf\u4e4b\u95f4\u7684\u4e24\u7c7b\u5173\u7cfb\uff1a\u51fd\u6570\u5173\u7cfb\u4e0e\u76f8\u5173\u5173\u7cfb<br \/>\n\u2461 \u5236\u4f5c\u6563\u70b9\u56fe\uff0c\u5224\u65ad\u7ebf\u6027\u76f8\u5173\u5173\u7cfb<br \/>\n\u2462 \u7ebf\u6027\u56de\u5f52\u65b9\u7a0b\uff1a$\\hat{y}=bx+a$ \uff08\u6700\u5c0f\u4e8c\u4e58\u6cd5\uff09<\/p>\n<p>$$<br \/>\nb = \\frac{\\sum_{i=1}^n x_iy<em>i &#8211; n\\overline{x}\\overline{y}}{\\sum<\/em>{i=1}^n x_i^2 &#8211; n\\overline{x}^2}<br \/>\n$$<\/p>\n<p>$$<br \/>\na = \\overline{y} &#8211; b\\overline{x}<br \/>\n$$<\/p>\n<blockquote>\n<p>\u6ce8\u610f\uff1a\u7ebf\u6027\u56de\u5f52\u76f4\u7ebf\u7ecf\u8fc7\u5b9a\u70b9$(\\overline{x}, \\overline{y})$<\/p>\n<\/blockquote>\n<h2>\u76f8\u5173\u5173\u7cfb<\/h2>\n<p>\u5b9a\u4e49\uff1a\u5982\u679c\u4e24\u4e2a\u53d8\u91cf\u4e2d\u4e00\u4e2a\u53d8\u91cf\u7684\u53d6\u503c\u4e00\u5b9a\u65f6\uff0c\u53e6\u4e00\u4e2a\u53d8\u91cf\u7684\u53d6\u503c\u5e26\u6709\u4e00\u5b9a\u7684\u968f\u673a\u6027\uff0c\u90a3\u4e48\u8fd9\u4e24\u4e2a\u53d8\u91cf\u4e4b\u95f4\u7684\u5173\u7cfb\uff0c\u53eb\u505a<strong>\u76f8\u5173\u5173\u7cfb<\/strong>\u3002<\/p>\n<p>\u4e24\u7c7b\u7279\u6b8a\u7684\u76f8\u5173\u5173\u7cfb\uff1a\u5982\u679c\u6563\u70b9\u56fe\u4e2d\u70b9\u7684\u5206\u5e03\u662f\u4ece<strong>\u5de6\u4e0b\u89d2<\/strong>\u5230<strong>\u53f3\u4e0a\u89d2<\/strong>\u7684\u533a\u57df\uff0c\u90a3\u4e48\u8fd9\u4e24\u4e2a\u53d8\u91cf\u7684\u76f8\u5173\u5173\u7cfb\u79f0\u4e3a<strong>\u6b63\u76f8\u5173<\/strong>\uff1b\u5982\u679c\u6563\u70b9\u56fe\u4e2d\u70b9\u7684\u5206\u5e03\u662f\u4ece<strong>\u5de6\u4e0a\u89d2<\/strong>\u5230<strong>\u53f3\u4e0b\u89d2<\/strong>\u7684\u533a\u57df\uff0c\u90a3\u4e48\u8fd9\u4e24\u4e2a\u53d8\u91cf\u7684\u76f8\u5173\u5173\u7cfb\u79f0\u4e3a<strong>\u8d1f\u76f8\u5173<\/strong>\u3002<\/p>\n<h2>\u7ebf\u6027\u76f8\u5173<\/h2>\n<p>\u5982\u679c\u4e24\u4e2a\u53d8\u91cf\u6563\u70b9\u56fe\u4e2d\u70b9\u7684\u5206\u5e03\u4ece\u6574\u4f53\u4e0a\u770b\u5927\u81f4\u5728\u4e00\u6761\u76f4\u7ebf\u9644\u8fd1\uff0c\u6211\u4eec\u5c31\u79f0\u8fd9\u4e24\u4e2a\u53d8\u91cf\u4e4b\u95f4\u5177\u6709<strong>\u7ebf\u6027\u76f8\u5173<\/strong>\u5173\u7cfb\uff0c\u8fd9\u6761\u76f4\u7ebf\u53eb\u505a<strong>\u56de\u5f52\u76f4\u7ebf<\/strong>\u3002<\/p>\n<p>\u6700\u5c0f\u4e8c\u4e58\u6cd5\uff1a\u6c42\u7ebf\u6027\u56de\u5f52\u76f4\u7ebf\u65b9\u7a0b$\\hat{y}=bx+a$\u65f6\uff0c\u4f7f\u5f97\u6837\u672c\u6570\u636e\u7684\u70b9\u5230\u5b83\u7684<strong>\u8ddd\u79bb\u7684\u5e73\u65b9\u548c<\/strong>\u6700\u5c0f\u7684\u65b9\u6cd5\u53eb\u505a\u6700\u5c0f\u4e8c\u4e58\u6cd5\uff0c\u5176\u4e2d$a$\uff0c$b$\u7684\u503c\u7531\u4ee5\u4e0b\u516c\u5f0f\u7ed9\u51fa\uff1a<\/p>\n<p>$$<br \/>\n\\hat{b} = \\frac{\\sum_{i=1}^n (x_i-\\overline{x})(y<em>i-\\overline{y})}{\\sum<\/em>{i=1}^n (x<em>i-\\overline{x})^2} = \\frac{\\sum<\/em>{i=1}^n x_iy<em>i &#8211; n\\overline{x}\\overline{y}}{\\sum<\/em>{i=1}^n x_i^2 &#8211; n\\overline{x}^2}<br \/>\n$$<\/p>\n<p>$$<br \/>\n\\hat{a} = \\overline{y} &#8211; \\hat{b} \\overline{x}<br \/>\n$$<\/p>\n<p>\u5176\u4e2d\uff0c$\\hat{b}$\u662f\u56de\u5f52\u65b9\u7a0b\u7684\u659c\u7387\uff0c$\\hat{a}$\u662f\u56de\u5f52\u65b9\u7a0b\u5728$y$\u8f74\u4e0a\u7684\u622a\u8ddd\u3002<\/p>\n<blockquote>\n<p>\u5f52\u7eb3\u603b\u7ed3\uff1a\u56de\u5f52\u76f4\u7ebf\u662f\u5bf9\u539f\u6570\u91cf\u5173\u7cfb\u7684\u4e00\u79cd\u62df\u5408\uff0c\u5982\u679c\u4e24\u4e2a\u53d8\u91cf\u4e0d\u5177\u6709\u7ebf\u6027\u76f8\u5173\u5173\u7cfb\uff0c\u5373\u4f7f\u6c42\u51fa\u56de\u5f52\u65b9\u7a0b\u4e5f\u662f\u6beb\u65e0\u610f\u4e49\u7684\uff0c\u800c\u4e14\u7531\u5176\u5f97\u5230\u4f30\u8ba1\u548c\u9884\u6d4b\u7684\u503c\u4e5f\u662f\u4e0d\u53ef\u4fe1\u7684\u3002<\/p>\n<\/blockquote>\n<h2>\u968f\u673a\u4e8b\u4ef6\u53ca\u5176\u6982\u7387<\/h2>\n<p>\u4e8b\u4ef6\uff1a\u8bd5\u9a8c\u7684\u6bcf\u4e00\u79cd\u53ef\u80fd\u7684\u7ed3\u679c\uff0c\u7528\u5927\u5199\u82f1\u6587\u5b57\u6bcd\u8868\u793a<\/p>\n<p>\u968f\u673a\u4e8b\u4ef6$A$\u7684\u6982\u7387\uff1a<\/p>\n<p>$$<br \/>\nP(A) = \\frac{m}{n}, \\, 0\u2264P(A)\u22641<br \/>\n$$<\/p>\n<h2>\u53e4\u5178\u6982\u578b<\/h2>\n<p>\uff081\uff09\u57fa\u672c\u4e8b\u4ef6\uff1a\u4e00\u6b21\u8bd5\u9a8c\u4e2d\u53ef\u80fd\u51fa\u73b0\u7684\u6bcf\u4e00\u4e2a\u57fa\u672c\u7ed3\u679c<br \/>\n\uff082\uff09\u53e4\u5178\u6982\u578b\u7684\u7279\u70b9<br \/>\n&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\u2460 \u6240\u6709\u7684\u57fa\u672c\u4e8b\u4ef6\u53ea\u6709\u6709\u9650\u4e2a<br \/>\n&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\u2461 \u6bcf\u4e2a\u57fa\u672c\u4e8b\u4ef6\u90fd\u662f\u7b49\u53ef\u80fd\u53d1\u751f<br \/>\n\uff083\uff09\u53e4\u5178\u6982\u578b\u6982\u7387\u8ba1\u7b97\u516c\u5f0f\uff1a\u4e00\u6b21\u8bd5\u9a8c\u7684\u7b49\u53ef\u80fd\u57fa\u672c\u4e8b\u4ef6\u5171\u6709$n$\u4e2a\uff0c\u4e8b\u4ef6$A$\u5305\u542b\u5176\u4e2d\u7684$m$\u4e2a\u57fa\u672c\u4e8b\u4ef6\uff0c\u5219\u4e8b\u4ef6$A$\u53d1\u751f\u7684\u6982\u7387\uff1a<\/p>\n<p>$$P(A)=\\frac{m}{n}$$<\/p>\n<h2>\u51e0\u4f55\u6982\u578b<\/h2>\n<p>\uff081\uff09\u51e0\u4f55\u6982\u578b\u7684\u7279\u70b9<br \/>\n&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\u2460 \u6240\u6709\u7684\u57fa\u672c\u4e8b\u4ef6\u662f\u65e0\u9650\u4e2a<br \/>\n&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\u2461 \u6bcf\u4e2a\u57fa\u672c\u4e8b\u4ef6\u90fd\u662f\u7b49\u53ef\u80fd\u53d1\u751f<br \/>\n\uff082\uff09\u51e0\u4f55\u6982\u578b\u6982\u7387\u8ba1\u7b97\u516c\u5f0f\uff1a<\/p>\n<p>$$P(A)=\\frac{d\u7684\u6d4b\u5ea6}{D\u7684\u6d4b\u5ea6}$$<\/p>\n<p>\u5176\u4e2d\u6d4b\u5ea6\u6839\u636e\u9898\u76ee\u786e\u5b9a\uff0c\u4e00\u822c\u4e3a\u7ebf\u6bb5\u3001\u89d2\u5ea6\u3001\u9762\u79ef\u3001\u4f53\u79ef\u7b49\u3002<\/p>\n<h2>\u4e92\u65a5\u4e8b\u4ef6<\/h2>\n<p>\uff081\uff09\u4e0d\u53ef\u80fd\u540c\u65f6\u53d1\u751f\u7684\u4e24\u4e2a\u4e8b\u4ef6\u6210\u4e3a\u4e92\u65a5\u4e8b\u4ef6<br \/>\n\uff082\uff09\u5982\u679c\u4e8b\u4ef6$A_1,A_2,\u00b7\u00b7\u00b7,A_n$\u4efb\u610f\u4e24\u4e2a\u90fd\u662f\u4e92\u65a5\u4e8b\u4ef6\uff0c\u5219\u79f0\u4e8b\u4ef6$A_1,A_2,\u00b7\u00b7\u00b7,A_n$\u5f7c\u6b64\u4e92\u65a5\u3002<br \/>\n\uff083\uff09\u5982\u679c\u4e8b\u4ef6$A$\uff0c$B$\u4e92\u65a5\uff0c\u90a3\u4e48\u4e8b\u4ef6$A+B$\u53d1\u751f\u7684\u6982\u7387\uff0c\u7b49\u4e8e\u4e8b\u4ef6$A$\uff0c$B$\u53d1\u751f\u7684\u6982\u7387\u7684\u548c\uff0c\u5373<\/p>\n<p>$$P(A+B)=P(A)+P(B)$$<\/p>\n<p>\uff084\uff09\u5982\u679c\u4e8b\u4ef6$A_1,A_2,\u00b7\u00b7\u00b7,A_n$\u5f7c\u6b64\u4e92\u65a5\uff0c\u5219\u6709\uff1a<\/p>\n<p>$$P(A_1+A_2+\u00b7\u00b7\u00b7+A_n)=P(A_1)+P(A_2)+\u00b7\u00b7\u00b7+P(A_n)$$<\/p>\n<p>\uff085\uff09\u5bf9\u7acb\u4e8b\u4ef6\uff1a\u4e24\u4e2a\u4e92\u65a5\u4e8b\u4ef6\u4e2d\u5fc5\u6709\u4e00\u4e2a\u8981\u53d1\u751f\uff0c\u5219\u79f0\u8fd9\u4e24\u4e2a\u4e8b\u4ef6\u4e3a\u5bf9\u7acb\u4e8b\u4ef6\u3002<br \/>\n&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\u2460 \u4e8b\u4ef6$A$\u7684\u5bf9\u7acb\u4e8b\u4ef6\u8bb0\u4f5c$\\overline{A}$\uff0c\u5373$P(A)+P(\\overline{A}),\\,P(\\overline{A})=1-P(A)$<br \/>\n&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\u2461 \u5bf9\u7acb\u4e8b\u4ef6\u4e00\u5b9a\u662f\u4e92\u65a5\u4e8b\u4ef6\uff0c\u4e92\u65a5\u4e8b\u4ef6\u672a\u5fc5\u662f\u5bf9\u7acb\u4e8b\u4ef6<\/p>\n<h2>\u76f8\u4e92\u72ec\u7acb\u4e8b\u4ef6<\/h2>\n<p>\u4e8b\u4ef6$A$\uff08\u6216$B$\uff09\u662f\u5426\u53d1\u751f\u5bf9\u4e8b\u4ef6$B$\uff08\u6216$A$\uff09\u53d1\u751f\u7684\u6982\u7387\u6ca1\u6709\u5f71\u54cd\uff0c\u5373\u5176\u4e2d\u4e00\u4e2a\u4e8b\u4ef6\u662f\u5426\u53d1\u751f\u5bf9\u53e6\u4e00\u4e2a\u4e8b\u4ef6\u53d1\u751f\u7684\u6982\u7387\u6ca1\u6709\u5f71\u54cd\u3002\u8fd9\u6837\u7684\u4e24\u4e2a\u4e8b\u4ef6\u53eb\u505a\u76f8\u4e92\u72ec\u7acb\u4e8b\u4ef6\u3002<\/p>\n<p>\u5f53$A$\u3001$B$\u662f\u76f8\u4e92\u72ec\u7acb\u4e8b\u4ef6\u65f6\uff0c\u90a3\u4e48\u4e8b\u4ef6$A\u00b7B$\u53d1\u751f\uff08\u5373$A$\u3001$B$\u540c\u65f6\u53d1\u751f\uff09\u7684\u6982\u7387\uff0c\u7b49\u4e8e\u4e8b\u4ef6$A$\u3001$B$\u5206\u522b\u53d1\u751f\u7684\u6982\u7387\u7684\u79ef\u3002\u5373<\/p>\n<p>$$P(A\u00b7B)=P(A)\u00b7P(B)$$<\/p>\n<p>\u82e5$A$\u3001$B$\u4e24\u4e8b\u4ef6\u76f8\u4e92\u72ec\u7acb\uff0c\u5219$A$\u4e0e$\\overline{B}$\u3001$\\overline{A}$\u4e0e$B$\u3001$\\overline{A}$\u4e0e$\\overline{B}$\u4e5f\u90fd\u662f\u76f8\u4e92\u72ec\u7acb\u7684\u3002<\/p>\n<h2>\u72ec\u7acb\u91cd\u590d\u8bd5\u9a8c<\/h2>\n<p>\uff081\uff09\u4e00\u822c\u5730\uff0c\u5728\u76f8\u540c\u6761\u4ef6\u4e0b\u91cd\u590d\u505a\u7684$n$\u6b21\u8bd5\u9a8c\u79f0\u4e3a$n$\u6b21\u72ec\u7acb\u91cd\u590d\u8bd5\u9a8c\u3002<br \/>\n\uff082\uff09\u72ec\u7acb\u91cd\u590d\u8bd5\u9a8c\u7684\u6982\u7387\u516c\u5f0f\uff1a\u5982\u679c\u57281\u6b21\u8bd5\u9a8c\u4e2d\u67d0\u4e8b\u4ef6\u53d1\u751f\u7684\u6982\u7387\u662f$p$\uff0c\u90a3\u4e48\u5728$n$\u6b21\u72ec\u7acb\u91cd\u590d\u8bd5\u9a8c\u4e2d\u8fd9\u4e2a\u8bd5\u9a8c\u6070\u597d\u53d1\u751f$k$\u6b21\u7684\u6982\u7387\u4e3a<\/p>\n<p>$$ P_n(k)=C_n^kp^k(1-p)^{n-k} \\,\\, (k=0,1,2,\u00b7\u00b7\u00b7n)$$<\/p>\n<h2>\u6761\u4ef6\u6982\u7387<\/h2>\n<p>\u5bf9\u4efb\u610f\u4e8b\u4ef6$A$\u548c\u4e8b\u4ef6$B$\uff0c\u5728\u5df2\u77e5\u4e8b\u4ef6$A$\u53d1\u751f\u7684\u6761\u4ef6\u4e0b\u4e8b\u4ef6$B$\u53d1\u751f\u7684\u6982\u7387\uff0c\u53eb\u505a\u6761\u4ef6\u6982\u7387\uff0c\u8bb0\u4f5c$P(B|A)$\uff0c\u8bfb\u4f5c$A$\u53d1\u751f\u7684\u6761\u4ef6\u4e0b$B$\u53d1\u751f\u7684\u6982\u7387\u3002<\/p>\n<p>$$<br \/>\nP(B|A) = \\frac{P(AB)}{P(A)}, \\, P(A)&gt;0<br \/>\n$$<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u57fa\u672c\u6982\u5ff5 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[&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[509],"tags":[],"class_list":["post-2125","post","type-post","status-publish","format-standard","hentry","category-mathematics-fundamentals"],"_links":{"self":[{"href":"https:\/\/www.appblog.cn\/index.php\/wp-json\/wp\/v2\/posts\/2125","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.appblog.cn\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.appblog.cn\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.appblog.cn\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.appblog.cn\/index.php\/wp-json\/wp\/v2\/comments?post=2125"}],"version-history":[{"count":0,"href":"https:\/\/www.appblog.cn\/index.php\/wp-json\/wp\/v2\/posts\/2125\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.appblog.cn\/index.php\/wp-json\/wp\/v2\/media?parent=2125"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.appblog.cn\/index.php\/wp-json\/wp\/v2\/categories?post=2125"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.appblog.cn\/index.php\/wp-json\/wp\/v2\/tags?post=2125"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}