SOLUTION: If S is a sample space and A and B are events, when are A and B i. Mutually exclusive? ii. Exhaustive? iii. Independent

Algebra ->  Probability-and-statistics -> SOLUTION: If S is a sample space and A and B are events, when are A and B i. Mutually exclusive? ii. Exhaustive? iii. Independent      Log On


   

Question 1184199: If S is a sample space and A and B are events, when are A and B
i. Mutually exclusive?
ii. Exhaustive?
iii. Independent
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
i. A and B are mutually exclusive if A ∩ B = Ø, or equivalently, P(A ∩ B) = 0, or equivalently, P(A ∪ B) = P(A) + P(B).

ii. A and B are exhaustive if A ∪ B = S.

iii. A and B are independent if P(A ∩ B) = P(A)*P(B), or equivalently, P(A) = P(A|B), or P(B) = P(B|A).