已知P(A上横杠)=0.3,P(B)=0.4,P(A(B上横杠)=0.5,求P(B|AUB上横杠)

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已知P(A上横杠)=0.3,P(B)=0.4,P(A(B上横杠)=0.5,求P(B|AUB上横杠)已知P(A上横杠)=0.3,P(B)=0.4,P(A(B上横杠)=0.5,求P(B|AUB上横杠)已知

已知P(A上横杠)=0.3,P(B)=0.4,P(A(B上横杠)=0.5,求P(B|AUB上横杠)
已知P(A上横杠)=0.3,P(B)=0.4,P(A(B上横杠)=0.5,求P(B|AUB上横杠)

已知P(A上横杠)=0.3,P(B)=0.4,P(A(B上横杠)=0.5,求P(B|AUB上横杠)
条件概率公式:P(A|B) = P(AB)/P(B)
要求P(B|AU(B上横杠))
先看其化为右边形式,应是P(B|AU(B上横杠))=P(AB)/P(AU(B上横杠))
由P(B)=0.4,P(A(B上横杠)=0.5知P(A(B上横杠))=0.3,
∴分子P(AB)=1-0.3=0.7
而分母P(AU(B上横杠))=p(A)+P(B上横杠)-P(A(B上横杠))=(1-0.3)+(1-0.4)-0.3=1
∴P(B|AU(B上横杠))=0.7