Question

If $P\left(A\right)=0.4$, $P\left(B\right)=0.8$ and $P\left(B|A\right)=0.6$, then $P\left(A\cup B\right)$ is equal to

• A. $0.24$
• B. $0.3$
• C. $0.48$
• D. $0.96$

Answer 1

Answer: (D)

$P\left(A\right)=0.4$,
$P\left(B\right)=0.8$,
$P\left(B|A\right)=0.6$
$P\left(A\cap B\right)=P\left(B|A\right)P\left(A\right)=0.6\times 0.4=0.24$
$\therefore P\left(A\cup B\right)=P\left(A\right)+P\left(B\right)-P\left(A\cap B\right)$
$=0.4+0.8-0.24$
$=0.96$