条件概率的定义：事件A在事件B发生的条件下的概率（我的理解） 那么是不是暗含：A是B的子集，即B包含A 在条件概率中事件B发生的概率一般要大于事件A发生的条件下事件...
\u6761\u4ef6\u6982\u7387\u4e2dP(AB)\u4e0eP(B|A\uff09\u7684\u533a\u522b\u4e24\u8005\u7684\u533a\u522b\u5c31\u5728\u4e8e\u5176\u5b9a\u4e49\uff1a
P\uff08AB\uff09\u662fAB\u540c\u65f6\u53d1\u751f\u7684\u6982\u7387\uff0c\u662f\u4ee5\u5168\u4f53\u4e8b\u4ef6\u4e3a100%\u6765\u8ba1\u7b97\u5176\u4e2dAB\u540c\u65f6\u53d1\u751f\u7684\u6982\u7387\u3002
P\uff08B|A\uff09\u662f\u5728\u5df2\u7ecf\u53d1\u751f\u4e86A\u4e8b\u4ef6\u7684\u524d\u63d0\u4e0b\uff0c\u518d\u53d1\u751fB\u4e8b\u4ef6\u7684\u6982\u7387\u3002\u662f\u4ee5\u6240\u6709\u53d1\u751fA\u4e8b\u4ef6\u4e3a100%\u6765\u8ba1\u7b97AB\u540c\u65f6\u53d1\u751f\u7684\u6982\u7387\u3002
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\u5b9a\u74062
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\u8bbe \uff0c \uff0c\u2026 \u4e3a\u4efb\u610fn \u4e2a\u4e8b\u4ef6\uff08n\u22652\uff09\u4e14
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\u4f60\u770b\uff0c\u7531\u5b9a\u4e49:P\uff08B|A\uff09=P(AB)/P(A)
\u5982\u679c\u201cP(B)>P(B|A)\u201d\u662f\u5bf9\u7684\uff0c\u5219\u6709\uff1a
P(B)>P(AB)/P(A) => P(A)P(B)>P(AB)
\u4f46\u662fP(A)P(B)\u4e0d\u4e00\u5b9a\u5927\u4e8eP(AB)\u7684\uff0c
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2\uff09\u3002\u5982\u679cA,B\u662f\u72ec\u7acb\u7684\uff0c\u90a3\u4e48P(AB)=P(A)P(B)
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绛旓細P锛圔A闈烇級=P锛圔-A锛=P锛圔-AB锛=P锛圔锛-P锛圓B锛=P锛圔锛=0.3锛涚敱棰樼洰涓鎴戜滑姹傜殑闂涓轰竴涓鏉′欢姒傜巼锛屽嵆鍦ㄤ簨浠A闈炵殑鏉′欢涓浜嬩欢B鍙戠敓鐨勬鐜囷紝鏍规嵁鏉′欢姒傜巼鍏紡鎴戜滑鍙互寰楀埌锛歅(B|A闈)=P锛圔A闈烇級/P锛圓闈烇級=0.3/锛1-0.4锛=0.5 鏉′欢姒傜巼鏄寚浜嬩欢A鍦鍙﹀涓涓簨浠禕宸茬粡鍙戠敓鏉′欢涓...
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绛旓細鏉′欢姒傜巼鐨勫熀鏈蹇碉細璁鹃殢鏈鸿瘯楠孍涓紝A鍜孊鏄袱涓簨浠讹紝涓擝骞堕潪涓嶅彲鑳戒簨浠讹紝鍗砅(B) > 0銆傛鏃讹紝鎴戜滑瀹氫箟涓鍦ㄤ簨浠禕鍙戠敓鐨勫墠鎻愪笅锛浜嬩欢A鍙戠敓鐨勬鐜囷紝鍗 P(A|B)銆傜洿瑙傚湴锛屾垜浠彲浠ュ熷姪闊︽仼鍥炬潵鐞嗚В锛岃繖涓鐜囩殑璁＄畻灏卞儚鍦B浜嬩欢鐨勬き鍦嗚寖鍥村唴瀵绘壘A浜嬩欢鐨勪氦闆嗛儴鍒嗭紝闄や互B浜嬩欢鏈韩鐨勬鐜囥傛潯浠舵鐜囩殑鎬ц川...
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绛旓細鏉′欢姒傜巼鎬ц川鍏紡涓冧釜锛岀ず渚嬪涓嬶細P(A|B)=P(A鈭〣)/P(B)锛 P(A|B)=P(B|A)锛0鈮(B|A)鈮1锛汸(A|B)=1if A and B are always true锛汸(A|B)=0if A and B are always false锛汸(A|B)=P(A)if B is always true锛汸(A|B)=P(B)if A is always true....
绛旓細鏉′欢姒傜巼瀹氫箟: 璁続銆丅鏄袱涓簨浠讹紝涓擯(A)>0锛屽垯绉癨\ P(B|A)=\frac{P(AB)}{P(A)}涓浜嬩欢A鍙戠敓鐨勬潯浠朵笅浜嬩欢B鐨勬潯浠舵鐜銆傛湰韬浜庢潯浠舵鐜囧苟娌℃湁浠涔堝ソ璇寸殑.鍏抽敭鏄殑鏄杩欎釜寮忓瓙杩涜鍙樺舰锛屽嵆鍙緱鍒姒傜巼鐨涔樻硶鍏紡锛歅(A)>0鏃讹紝鍒橮(AB)=P(A)P(B|A)锛沑\ P(B)>0鏃讹紝鍒橮(AB)=...
