Question

If A and B are two events such that P(A) = 0.4, P(B) = 0.8 and $P\left(\frac{B}{A}\right)$ = 0.6, find P(A $\cup$ B)

• A. 0.24
• B. 0.96
• C. 0.04
• D. none of these

Answer 1

The correct option is B

0.96

$P\left(\frac{B}{A}\right)=0.6=\frac{P(A\cap B)}{P\left(A\right)}$
$0.6=\frac{P(A\cap B)}{0.4}$
$\Rightarrow P(A\cap B)=0.6\times 0.4$
$=0.24$
$P(A\cup B)=P\left(A\right)+P\left(B\right)-P(A\cap B)$
$=0.4+0.8-0.24$
$=0.96$