Question

Probability $P\left(A\right)=0.7,P\left(B\right)=0.4,P(A\cap B)=0.3$, then $P(A\cap B^{\prime })$ is equal to

• A. $0.1$
• B. $0.3$
• C. $0.2$
• D. $0.4$

Answer 1

The correct option is D $0.4$

Given, $P\left(A\right)=0.7,P\left(B\right)=0.4$

and $P(A\cap B)=0.3$

We know that,

$P(A\cup B)=P\left(A\right)+P\left(B\right)-P(A\cap B)$

$\Rightarrow P(A\cup B)=0.7+0.4-0.3=0.8$

Now, $P(A\cap B^{\prime })=P(A\cup B)-P\left(B\right)$ $=0.8-0.4=0.4$