Question

If $A$ and $B$ are two events, then which one of the following is not always true

• A. $P(A\cap B)\ge P\left(A\right)+P\left(B\right)-1$
• B. $P(A\cap B)\le P\left(A\right)$
• C. $P(A^{\prime }\cap B^{\prime })\ge P\left(A^{\prime }\right)+P\left(B^{\prime }\right)-1$
• D. $P(A\cap B)=P\left(A\right)\cdot P\left(B\right)$

Answer 1

The correct option is D $P(A\cap B)=P\left(A\right)\cdot P\left(B\right)$

If A and B are two independent events, then only
$P(A\cap B)=P\left(A\right)\cdot P\left(B\right)$ is true otherwise this is not true