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first prove *: if A intersect B is independent, then A intersect B' is independent. (this is on wiki answers)

P(A' intersect B') = P(B')P(A'|B') by definition

= P(B')[1-P(A|B')] since 1 = P(A) + P(A')

= P(B')[1 - P(A)] from the first proof *

= P(B')P(A') since 1 = P(A) + P(A')

conclude with P(A' intersect B') = P(B')P(A') and is therefore independent by definition.

***note*** i am a student in my first semester of probability so this may be incorrect, but i used the first proof* so i figured i would proof this one to kinda "give back".

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15y ago

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