please explain the question in the attached picture.

CB

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- Jul 8th 2007, 06:10 PMcomputer-botSets
please explain the question in the attached picture.

CB - Jul 8th 2007, 06:45 PMle_su14
$\displaystyle (A \cap B) \cup (A-(A \cap B)) = A$

Because :$\displaystyle (A \cap B) and (A-(A \cap B)) $ are mutually exclusive .

$\displaystyle So , P((A \cap B) \cup A-(A \cap B)) = P(A \cap B) + P(A-(A \cap B)) = P(A) $

and , $\displaystyle P(X) >= 0 $, with every events .

Therefore , $\displaystyle P(A \cap B) =< P(A)$