Question

If $A$ and $B$ are two events such that $P\left(A\right)=0.4,P(A\cup B)=0.7$ and $P(A\cap B)=0.2$ then $P\left(B\right)$ is equal to

• A. $0.1$
• B. $0.3$
• C. $0.5$
• D. $1$

Answer 1

The correct option is C $0.5$

We have,

$P\left(A\right)=0.4$

$P\left(B\right)=?$

$P(A\cup B)=0.7$

$P(A\cap B)=0.2$

Then,

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

$0.7=0.4+P\left(B\right)-0.2$

$0.7=0.2+P\left(B\right)$

$P\left(B\right)=0.7-0.2$

$P\left(B\right)=0.5$

Hence, this is the answer.