Question

If A and B are two events such that $P(A\cup B)=P(A\cap B),$ then the true relation is

• A.
• B.
• C.
• D. None of these

Answer 1

The correct option is C

$P(A\cup B)=P\left(A\right)+P\left(B\right)-P(A\cap B)$
$\Rightarrow P(A\cap B)=P\left(A\right)+P\left(B\right)-P(A\cap B)$
$\{\because P(A\cap B)=P(A\cup B\left)\right\}$
$\Rightarrow 2P(A\cap B)=P\left(A\right)+P\left(B\right)$
$\Rightarrow 2P\left(A\right).\frac{P(A\cap B)}{P\left(A\right)}=P\left(A\right)+P\left(B\right)$
$\Rightarrow 2P\left(A\right).P\frac{B}{A}=P\left(A\right)+P\left(B\right)$