Question

概率论试题

概率论试题求过程 谢谢

Answer 1

根据公式P(B|A)=P(AB)/P(A),P(A∪B)=P(A)+P(B)－P(AB)
则P(B|AUB')=P[(AUB')B]/P(AUB')=P(AB)/[P(A)+P(B')－P(AB')]
=[P(A)－P(AB')]/[P(A)+P(B')－P(AB')]=(1-0.2-0.5)/(1-0.2+1-0.4-0.5)=0.3/0.9=1/3

Answer 2

P(~A)=0.2, P(B)=0.4, P(A∩~B)=0.5
To find: P(B|AU~B)
Solution :
P(A∩~B)=0.5
P(A)-P(A∩B)=0.5
1-0.2 -P(A∩B)=0.5
P(A∩B)=0.3
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I= 全集
P(B|AU~B)
=P(B∩(AU~B)) /P(AU~B)
=P(B∩(I-B+A∩B)) /P(I-B+A∩B))
=P(A∩B) /( 1-P(B)+P(A∩B))
=0.3/(1-0.4+0.3)
=0.3/0.9
=1/3

Answer 3

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