Question

PROVE THAT FOR ANY TWO EVENTS A AND B ,WE HAVE P(AB)<=P(A+B)<=P(A)+P(B),WHERE P(A)AND P(B)ARE PROBABILITIES OF OCCURENCE OF EVENTS A AND B

Answer 1

I asume by \(P(A+B)\) you mean \(P(A\cup B)\)


\[A\cap B\subseteq A\cup B\]

therefore

\[P(A\cap B)\le P(A\cup B)\]

and

\[P(A\cup B)=P(A)+P(B)-P(A\cap B)\le P(A)+P(B)\]