Question

大学概率论：设A,B相互独立,P（A）=0.7,P(A∪B)=0.8,求P(B),P(AB),P(A-B).请给过程,谢

Answer 1

A,B相互独立 => P(AB) = P(A)*P(B) => P(AB) = 0.7P(B) (1)

P(A) = P(A-B) + P(AB) => 0.7 = P(A-B) + P(AB) (2)

P(A∪B)= P(A-B)+P(B) => 0.8= P(A-B)+P(B) (3)

(1)(2)(3) =>

P(B) =1/3

P(AB) = 7/30

P(A-B) = 7/15