Question

If $P\left(A\right)=0.8,P\left(B\right)=0.5$ and $P\left(B/A\right)=0.4$, then the value of $P(A\cup B)$ is:

• A. $0.95$
• B. $0.12$
• C. $0.78$
• D. $0.98$

Answer 1

The correct option is D $0.98$

Given: $P\left(B/A\right)=0.4$
$\Rightarrow 0.4=\frac{P(A\cap B)}{P\left(A\right)}$
$\Rightarrow P(A\cap B)=0.32$
Now, $\therefore P(A\cup B)=P\left(A\right)+P\left(B\right)-P(A\cap B)$
Substituting the values we get
$\Rightarrow P(A\cup B)=0.8+0.5-0.32=1.3-0.32$
$\Rightarrow P(A\cup B)=0.98$