Sets

Quote:

Originally Posted by computer-bot

please explain the question in the attached picture.

CB

$(A \cap B) \cup (A-(A \cap B)) = A$
Because : $(A \cap B) and (A-(A \cap B))$ are mutually exclusive .
$So , P((A \cap B) \cup A-(A \cap B)) = P(A \cap B) + P(A-(A \cap B)) = P(A)$
and , $P(X) >= 0$ , with every events .
Therefore , $P(A \cap B) =< P(A)$