Browse Questions

# Check whether the following probabilities P(A) and P(B) are consistently defined .$P(A)=0.5,P(B)=0.4,P(A \cup B)=0.8$

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

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)
Step 1:
$P(A)=0.5$
$P(B)=0.4$
$P(A\cup B)=0.8$
$\therefore P(A \cup B)=P(A)+P(B)-P(A\cap B)$
$0.8=0.5+0.4-P(A \cap B)$
Step 2:
$P(A \cap B)=0.5+0.4-0.8$
$\Rightarrow 0.9-0.8$
$\Rightarrow 0.1$
$\Rightarrow P(A\cap B) < P(A)$ and $P(B)$
$\therefore$ Given data are consistent
Hence (A) is the correct answer.