Browse Questions

# If $A\cup B)=P(A \cap B)$ for any two events A and B,then

$\begin{array}{1 1}(A)\;P(A)=P(B)\\(B)\;P(A) > P(B)\\(C)\;P(A) < P(B)\\(D)\;\text{None of these}\end{array}$

Toolbox:
• $P(A \cup B)=P(A)+P(B)-P(A \cap B)$
Given : $P(A \cup B)=P(A \cap B)$
We know that
$P(A \cup B)=P(A)+P(B)-P(A \cap B)$
Replacing
$P(A \cup B)=P(A)+P(B)-P(A \cup B)$
$2P(A \cup B)=P(A)+P(B)$
Or $2P(A \cap B)=P(A)+P(B)$
$\Rightarrow P(A) =P(B)$
Hence (A) is the correct answer.