Question

If $A$ and $B$ are independent events such that $P(A\cup B)=0.6,P\left(A\right)=0.2$, find P(B).

Answer 1

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

$0.6=0.2+P\left(B\right)-P(A\cap B)$

$\Rightarrow P\left(B\right)-P(A\cap B)=0.6-0.2=0.4$

Since $A$ and $B$ are independent,

$P(A\cap B)=P\left(A\right)\times P\left(B\right)$

$\Rightarrow P(A\cap B)=0.2\times P\left(B\right)$

Therefore,

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

$\Rightarrow P\left(B\right)=\frac{0.4}{0.8}=0.5$