# Check whether the following probabilities P(A) and P(B) are consistently defined .$P(A)=0.5,P(B)=0.7,P(A \cap B)=0.6$

$\begin{array}{1 1}(A)\;\text{Consistent}\\(B)\;\text{Not consistent}\end{array}$

Toolbox:
• The formula used to solve the problem $P(A \cup B)=P(A)+P(B)-P(A\cap B)$
• For consistent $P(A \cap B)$ must be less than or equal to P(A) and P(B)
$P(A)=0.5$
$P(B)=0.7$
$P(A\cap B)=0.6$
From the given probabilities
$P(A \cap B)$ is not less than or equal to P(A)
(i.e) $P(A\cap B)\nleq P(A)$
$\therefore$ Given data is not consistent.
Hence (B) is the correct answer.